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# Ejected Electrons: Newsletter Challenge (11/06/07)

Posted November 11, 2007 5:01 PM
Pathfinder Tags: challenge questions

The question as it appears in the 11/13 edition of Specs & Techs from GlobalSpec:

Electrons are ejected from the surface of a metal plate exposed to light with wavelength . A uniform, retarding electric field E is imposed on the plate, and it is observed that the ejected electrons do not travel more than a distance d from the surface of the plate. What is the threshold wavelength for the plate material?

(Update: Nov 20, 8:49 AM EST) And the Answer is...

The threshold wavelength is defined as the minimum wavelength capable of ejecting electron form the metal plate. This wavelength, , is a material property.

When light of wavelength impinges on the surface of the plate the ejected electrons will acquire a kinetic energy equal to

(1)

When the electrons move in the direction of the retarding electric field and reach the maximum distance d, all this energy is converted into potential energy given by

(2)

Equating equations (1) and (2), we get

(3)

Solving for we get

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#1

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 9:53 AM

I am just a simple Mechanical Engineer. I am sitting this one out. Have fun Fyz!

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#3

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 9:56 AM

Just balance energies, and it's straightforward.

Fyz

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#66

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 3:18 PM

It's not easy at all! I can't pick up individual electrons with these claws!

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#2

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 9:53 AM

λ0 ≈ 1/(1/λ-d.E.q/c/h)

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#4

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 11:35 PM

Yes, I concur. but also clarify q is charge on electron, c is velocity of light and h is Planck's constant.

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#5

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 11:39 PM

Also Final term under line should read d.E.q/c.h

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#6

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/12/2007 11:45 PM

to be very specific d.E.q/(c.h)

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#15

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:09 AM

So why change it?

[I believe that 1/(c.h) is just a different way of writing 1/c/h (or vice versa) ]

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#17

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:17 AM

Clarity!

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#20

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:49 AM

Doesn't "should read" imply that the original was wrong? [It would be fine to say "easier to read as" or something similar]. BTW, some types of photo-cathode don't behave quite as this would suggest - I'll go into some detail when I have time.

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#29

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:46 AM

Do you mean:

1/(c.h) == h/c ?

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#42

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 3:09 PM

I meant what I wrote. I'm not sure what the expression you wrote means (is this another editor issue?).

If the statement is true, it needs to be true for any numbers. So, just to illustrate with arbitrary (simple) numbers, I substitute c=3 and h=5. The left side of your expression is 1/(c.h) = 1/(3.5) = 1/15 ≈ 0.0667. The right hand side is 3/5 = 0.6

It's all down to the way the associations (interactions) between algebraic operators are defined.

Using the same numbers to illustrate some of the range of true identities: the standard definitions mean that 1/5/3 ≡ (1/5)/3 ≡ 1/15 ≡ 1/(3.5) ≡ (1/3)/5 ≡ 1/3/5. Clearly 1/5/3 ≠ 1/(5/3), for example. The use of the identity sign** rather than the equality sign is to indicate that these expressions are identical by virtue of the definition of the functions, rather than merely being of equal value.

**(I used the blue Omega signal on the task bar to give the list of symbols)

I hope that's of some help

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#47

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:10 PM

Fyz,

It's tangles like these that prompted my Clarity! comment. Bung in enough sets of parentheses so that there can be no ambiguity.

BTW Did you ever have a Sinclair Scientific calculator? The input was in reverse Polish notation, which limited the use to folk who really wanted or needed one (not as a 'fashion statement' or whatever).

John

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#48

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:39 PM

Meant to add/edit, but ran out of time: clarity in the layout of a calculation was essential for RPN to work - Sinclair's machine helped me sort out the way a sum should be ordered.

Didn't realise 'til years later that I was doing the work any self-respecting compiler should be doing for me. Getting a compiler's worth of programming into a cheapo pocket calculator wasn't an option in those days.

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#49

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:41 PM

Hi JohnDG,

My HP 28S calculator uses RPN and I love it.

-John

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#50

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:50 PM

Do the valves (US: tubes) get very hot?

Must agree I used to enjoy using the Sinclair.

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### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 9:05 PM

"Do the valves (US: tubes) get very hot?"

Yes! I sometimes use it for a handwarmer on cold job sites.

Really though, once you get used to RPN it seems quite natural. I used to get confused when switching back to a "generic" calculator after using the HP for a while.

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#53

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 2:23 AM

Yes! If all those fading-Nancys out there had to apply RPN they would realize how useful it really is. That's why I paid bucks for a replacement HP 15c on eBay and have an emulator on my desktop!

That's probably also why I found FORTH so easy and intuitive to use... Same basic structure! Also why when you drop into a Sparc-station's guts you find the whole operating system is written in FORTH - the same thing for a Mac, but if you get that low in a Mac, it's probably because your hard drive is fried.

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#64

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 1:57 PM

Hi vermin,

I was going to bring up FORTH but you beat me to it. Dang you!

How does the emulator work on your PC? What do you use it for? Is it freeware?

Cheers,

-John

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#75

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 1:21 AM

Some guy out there created an HP 15C emulator that looks exactly like the calculator, and it doesn't have the 2.2 In/e bug. I think I paid \$29.99 for it, but that was voluntary.

It's exactly like an HP 15C on my screen. I don't like the later versions of calculators by HP. They're all graphing calculators. And make it difficult just to do simple equations!!! That's why I found an HP 15C - no graphics. Just numbers, that's how I think!!!

It still does integrals, and allows you to work with imaginary numbers. As far as graphing, I'll save that for my 24" wide PC screen, not the little screen on some funky, little, HP graphic calculators.

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#56

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 7:32 AM

No, I had been using a(n) HP35 for a few years by the time that was introduced. My original had the "2.02/ln/exp = 2 bug", and I accepted HP's offer to change it (I rather wish I'd been rich enough to buy the corrected one and swap it for my company's faulty one instead - it's a significant piece of history).

From my point of view, Reverse Polish is a far better system for a calculator than standard algebraic notation. It requires fewer fewer keystrokes for one thing; and, if you are working a problem without writing it on paper first, you can enter the numbers while you are working out the algorithm. (I think it would also be better for text than standard notation - but it's hard to change)

On the other hand, in spite of many innovations, the Sinclair scientific would not have suited. Partly the keyboard, but I think there was also an issue with the limited depth of the push-down stack

What really amazes me is hearing complaints about both reverse polish and the latest fully algebraic calculators from people who've become used to the "mixed" mode of calculator (that used forward for addition, subtraction, etc, but reverse for sin, cos, etc)

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#59

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 11:01 AM

Is this the same logic as is/was used on the Texas Instruments calculaters in the 80s? Mum bought me one at senior school and I loved it, coz it demanded numbers & commands were entered (to me) in the right order. All my replacement calculators were TI, until I needed a cheap one for work (under Â£5!), when I ended up with a Casio. I still hate using Casios...

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#60

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 11:45 AM

Yes, both HP and the (later, cheaper, and extended-battery-life) TI scientific calculators used reverse polish notation.

It's a weird thought that you have to have a cheaper calculator for work than you did at school/university. Can't you find a less kleptocratic working environment?

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#67

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 3:21 PM

"both HP and the (later, cheaper, and extended-battery-life) TI scientific calculators used reverse polish notation."

Possibly, but all the TI calculators I ever owned, and I owned quite a few in the 70's , 80's, and 90's after my expensive HP-45 was stolen in 1975, had algebraic notation. I don't even own one now. Any calculations I must do that are not on a spreadsheet I use the MS Calculator that comes with Windows, and it is NOT RPN.

Perhaps the more advanced TI "programmable" calculators use RPN, but AFAIK, all the basic scientific units are algebraic.

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#68

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 4:01 PM

The popular SR50 and SR51 (I think I've got the numbers right) TI calculators were what I would describe as hybrids - +-x/^ were entered in standard algebraic (Polish) notation, but trig functions, exponents, etc were performed on the displayed number. That's just the same as the "scientific" calculator that Microsoft provide as a windows accessory. But there were also rpn calculators other than HP's and Sinclair's. I thought they were an option from TI, but I never needed one so I can't be certain (I kept the HP45 until I moved to a programmable - also rpn). What I do know is that none of the people I worked with before 1980 used an "algebraic" calculator.

Older calculators from Casio were also the same as Microsoft. The recent machines from Casio are pure algebraic. I think the "attraction" is that they display the equation just like it was copied from the textbook, so any dumkopf can copy and/or check the equation is correct. Unfortunately, that results in even greater use of brackets than the already yucky older arrangements - to my way of thinking totally unusable for anything serious - yukN!

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#79

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 9:46 AM

What I do know is that none of the people I worked with before 1980 used an "algebraic" calculator

Quite possible, but poor college students often could not afford the HP's and others of that ilk. I saw and used plenty of TI SR-10, SR-11, and later SR-40 and SR-50 calculators at engineering school in the mid to late 70's. If you want to call those "hybrids" because trig function and exponents were performed directly, fine. However, even in algebraic formulas trig functions and exponents apply directly to the numbers/variables without parentheses or "equals" signs. I don't believe Casio calculators ever required an "=" sign or parentheses for those functions either.

When I graduated from high school in 1974 our senior AP/Honors science class ("Advanced Placement", independent study/research/seminars taught/led by the school's Physics teacher) honored our soon-to-retire mentor by visiting him at his home in the country after graduation, before we all left for college. He had always chastised us as being "lazy birds" for using electronic calculators, never owned one himself, since slide rules gave answers that were "close enough". We pitched in and (partly as a joke) bought him a TI SR(for "slide rule"?)-11 "scientific calculator" which was about \$100 at the time. We handed him the wrapped present and his eye's began to well up. We were kind of found of this old curmudgeon, and, apparently, he of us as well. When he saw what it was he started laughing, but all he could get out was, "....you crazy Birds!" with a big grin on his face!

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#82

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 11:33 AM

They didn't; but I understand* some of the newst ones enter just like writing the equations. Standardisation of a sort, but pretty dumb nonetheless once the other method is established.

*but I'm not about to contribute to Casio's profits just to check.

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#63

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 1:30 PM

I hate Casios to; trouble is they seem to have cornered the market at most of the retail outlets round here. I've got an fx-991MS, but if I'm antwhere near a PC, I'd much rather use something on that (either MS calculator, Excel, or (if it's my PC) even one of the VB apps I've cobbled up for specific tasks). I've played with the PowerToy calc, but I'm not keen on it.

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#65

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 3:14 PM

ER, I think you might be a bit confused. Reverse Polish Notation was at one time the standard for HP calculators (In 1974 I had an HP-45, basically a jazzed up HP-35). These calculators use an "ENTER" key for data, and you did not commit to which operation would be done until it was to be done, unlike the TI calculators which, same as Casio, use "normal" algebraic notation. So on TI, Casio, etc. you would be required to use parentheses in entering a formula that required a sub-operation to be performed to the right of a previously entered operation, example:

2 x 3 + 4 = 10 (six keystrokes) but if what you wanted was 2 x (3 + 4) = 14 you had to use the parentheses and 8 keystrokes.

In RPN you enter numbers in a stack of registers, just like a computer does, so CompSci and Software Engineers just loved it. Example:

2 ENTER 3 x 4 + would result in the first answer, 10, with the same number of keystrokes, but if you wanted the second you would use 2 ENTER 3 ENTER 4 + x to get the second answer, 14 in 7 keystrokes.

Notice something? You used one less keystroke then the TI method. On really hairy computations the reduced number of keystrokes could really add up, speeding the computation, but you really had to know what you were doing, as it could be easy to make a mistake. The TI method became known as "Algebraic" since it allowed one to enter expressions pretty much as written, whereas RPN sometimes required one to juggle the numbers, depending on how many levels of "stack registers" were available. Algebraic notation could lead to mistakes as well, especially if there were many nested parentheses and one (left or right) got missed along the way.

No, this discussion is mostly regarding so-called "scientific calculators" as opposed to electronic versions of the formerly mechanical "adding machines" (of which TI did make many models) which were common in business at that time. Electronic adding machines basically entered series of numbers, each followed by an operation, usually addition or subtraction, with multiplication and division being added later, as well as multiplication by some previously stored constant, K. One did not always need the "=" key, because the machine displayed the running total, but it was used if there some final multiplication/division operation(s) done on total. They could be used for elementary computations as well, but were not well suited for anything more complex than that. In some ways this procedure resembled the RPN notation, there was usually an "enter" key as well, but these simple machine did not have the multiple registers which the powerful HP and other RPN calculators used. An RPN machine did NOT have the "=" key.

Interestingly, just as today the personal computer field is divided in to "Mac" people and "PC" people, the hand calculator world also was divided into "TI" guys and "HP" guys, with many finding it almost impossible to quickly adapt to the other system. Many a study lounge or university center heard similar requests, like "Hey, can I borrow your calculator? Oh, its a _________ ? Nevermind. I (Pick one: can't / don't know how to / don't like to) work one of those." Funny thing is, the arguably superior HP with RPN, like the Mac, seems to have lost out to the ubiquitous and arguably less powerful (like the PC) TI/Casio with "algebraic" notation. Is this just another example of "dumbing" down, or a salute to the power of mass marketing (or both)?

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#78

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 8:02 AM

It is interesting to remember the OLD days. Physicist talks about the SR-51, I had one and it served it's propose well. Today though I do a lot of repetitive work and the spreed sheet has turned out to be the best tool for that. I create a template with the formulas and just keep copying it. I can also copy the data in from a database and make the data entry easier.

You mention the MAC, I do like the MAC, but it had a lot more horsepower when they were using Motorola chips, so the big advantage of going with a MAC disappeared when they started putting Intel under the hood. Still have a G4 and it runs great.

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#72

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 12:52 AM

Whenever I thought about the layout of a complicated equation, with multiple "par-ens" and such, it always seemed to me that using RPN allowed me to put it together on the calculator just like I would have done with a pencil and paper. The other calculators always had me forcing some intermediate value into memory, doing another operation and then retrieving from memory to continue.

Whether the rest of the world likes it or not, if you see equations in your head, RPN works far better than the other messed up way of looking at math! But, then again, I also have stated that I really like FORTH, as well.

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#57

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 7:36 AM

Oh, and there's no ambiguity there. Unnecessary brackets just take longer to assimilate. Plus you can still write different orders. But things are easier to read if you can use full width horizontal lines for division (damn the editors, though...)

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#46

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 6:39 PM

Hi Fyz,

I agree with you. I was merely trying to avoid the confusion of those people who might read his original:-

λ0 ≈ 1/(1/λ-d.E.q/c/h)

as being equivalent to :-

λ0 ≈ 1/(1/λ-d.E.q.h/c)

like if you divide x by 3/5 it's the same as multiplying x by 5/3

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#7

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 12:57 AM

I did a nicely-formatted piece on Word 2007 using the Equation Editor. I've saved it in various HTML formats, then tried to cut-and-paste it as HTML to CR4's editor, but to no avail. I've tried everything I can think of, but none of the equations show up; just the text.

I'm so frustrated with CR4's primitive editor I could just scream. What's engineering without equations?

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#8

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 1:02 AM

Mechanics?

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#19

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:46 AM

You've done it again mate!

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#9

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 1:30 AM

is it possible to do a screen capture and save it as a jpg/gif and link it in the web page?

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#24

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 7:38 AM

It is possible (and quite simple):

With what you want displayed on screen, hit the PrintScreen button (upper right-hand corner of keyboard). Open a session of "Paint" and paste (Ctl-V). You can edit and save the image.

regards,

R.

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#28

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 8:46 AM

I'll give it a shot. Thanks.

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#30

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 10:25 AM

Hi Rick,

I tried using Paint, but found a more convenient method to convert the piece into a series of JPEGs. Microsoft Word 2007 has a plugin that allows one to save a document as a PDF. I then took the PDF over to my Mac, opened it with Preview, then saved each page as a JPEG. There is probably a better way but, as Ky suggests, I may be "primitive."

Anyway, I hope these images are visible where the equations in my other post were not. The JPEGs I uploaded to CR4 have very good resolution and are very easy to read, but CR4's magic shrinks them almost to the point where these images are illegible.

As always, peer-review of anything I post here is most welcome.

Page 1/3:

Page 2/3:

Page 3/3:

-e

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#34

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 10:58 AM

Hi Europium,

Looks a lot better. This method will work fine for any WORD document, I agree. I use the "Print-Screen"/Paint method on any and everything though. Whenever I go on a website and need a pic with its accompanying text, I find it is a quick and easy way to keep and insert into whatever doc/email I'm working with. I even got "short-keys" to open paint as to make the process faster (Then again, process is my game).

Glad you found a easier way...

regards,

R.

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#35

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 11:01 AM

Thanks for the suggestion.

One thing I ran into with Paint is that I could not copy the entire piece into Paint as a single image. Trying to resize Paint's "canvas" to accommodate the larger image was a pain in the ass and never did work quite right. I tried copying and pasting each page into Paint, but this, too, was frustrating.

Nevertheless I will use your method for smaller images.

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#41

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 2:48 PM

I agree - for the majority of surfaces (i.e where such calculations can be valid). But it escapes me why you wish to convert kinetic energy to velocity and back again. To my way of thinking, all that happens is that the electrons reverse direction when the potential energy acquired is equal to the original kinetic energy - and this would still be as true if the energies were so high that the electron velocities became relativistic.

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#43

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 5:02 PM

Hi Phyz,

I'm sure the path to the solution isn't optimal and that a better and perhaps simpler approach could be taken. But it worked.

Why did I use velocities? Simply because they show up in the more straightforward calculations of kinetic energy, and because they function as a kind 'lingua franca' to establish equivalence between certain relationships. But as you can see from my derivation, they're also eliminated in short order. I am certain there are better and more elegant ways to do this!

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#44

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 5:27 PM

I imagine you are saying it's the easiest way to explain to the widest range of disciplines - which is fare** enough.

**perhaps we've milked the basic calculation for all it is worth. Do you suppose it's worth addressing the additional complexities of surface potential barriers and/or channelled crystalline photo-cathodes, or would this only cause (even more) confusion?

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#45

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 6:08 PM

How's about you do that part? I'm familiar with the photoelectric effect generally, but I'm not familiar with specific material-science aspects as you've mentioned.

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#54

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 4:24 AM

peer review, I've peered hard at it and I still can't quite read it.

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#21

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 5:05 AM

Vermin was so right. To the spot. But I understand what your real point was. I attached a dig. photo of a hand written formula the other day because it was the fastest way known to me to get it out there. The ones in the know (of formulas) will appreciate. The ones with a "Canon" can shoot whatever comes to mind. If you have such a tool why not use it. Or are you yourself the primitive.

"I'm so frustrated with CR4's primitive editor I could just scream."

Besides, I could be the ignorant. Gosh I love this hobby. Sorry to interrupt. Ky.

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#25

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 7:39 AM

Europium,

Look at post #24 to ease some of the frustrations....

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#10

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 1:38 AM

Note: Here's what CR4's editor does to an HTML document that looks just fine on any other HTML browser on the planet. My apologies for such a dismal-looking layout, but it can't be helped...

-e

-----

Electrons are ejected from the surface of a metal plate exposed to light with wavelength . A uniform, retarding electric field E is imposed on the plate, and it is observed that the ejected electrons do not travel more than a distance d from the surface of the plate. What is the threshold wavelength for the plate material?

-----

The force on an electron of charge in a uniform electric field of strength is given by

(1)

But as force is also equal to mass times acceleration, we also have, for a non-relativistic electron,

(2)

where is the electron rest mass and is the acceleration under the influence of a uniform electric field . Equating (1) and (2), above, and solving for , we get

(3)

Given the well-known relations (from Phys 101) between distance (), acceleration () and velocity ():

(4)

and

(5)

we eliminate and solve for

(6)

But as

We substitute (3) for in (6), yielding

(7)

Now we digress for a moment and discuss the "work function" which describes the minimum photon energy required to dislodge an electron from a metal:

(8)

where is Planck's constant and is the frequency of the photon.

A photon of frequency having energy in excess of will possess a kinetic energy . Consequently

(9)

where

(10)

But as

(11a)

and similarly

(11b)

we get

(12)

We then substitute (7) into (10) to eliminate , thereby obtaining the kinetic energy of the electron in terms of electric field strength, electron charge, electron mass and distance from metal plate:

hence

(13)

Substituting (13) into (12), we get

(14)

Finally we solve for

and lastly

(15)

Q.E.D

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#11

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 1:55 AM

Ya know, somehow this is strangely understandable without the equations.

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#12

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 2:01 AM

Note: Here's what CR4's editor does to an HTML document that looks just fine on any other HTML browser on the planet. My apologies for such a dismal-looking layout, but it can't be helped...

-e

-----

Electrons are ejected from the surface of a metal plate exposed to light with wavelength . A uniform, retarding electric field E is imposed on the plate, and it is observed that the ejected electrons do not travel more than a distance d from the surface of the plate. What is the threshold wavelength for the plate material?

we get

(12)

(14)

and lastly

(15)

Q.E.D

---

I think this works just as well!!!

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#13

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 2:26 AM

Errata: Invert the right-hand side of (15).

I am my own worst proofreader.

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#14

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 2:29 AM

Woof!!! That explains it all!!!

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#31

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 10:29 AM

Equation (15) has been fixed in Post #30

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#16

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:13 AM

I'm seeing some text & lots of windows placeholders but no pictures from europium & vermin.

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#18

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 4:22 AM

Complain to Chris L.

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#22

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 5:17 AM

you mean of them? They could have been hit with the 'ugly stick', so we don't want that to come out!

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#26

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 7:48 AM

In defense of their editor, trying to link speciality applications is tricky because for somebody else to view it, they would have to have a copy of your program. Also various different operating systems treat these speciality links differently so if you developed your equation in a Linux environment, it may not work in either Unix or MAC or MS Windows. Best way to avoid this is to go with a standard format such as a JPG.

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#33

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 10:54 AM

Yes, but I tried saving the file as HTML, which CR4's editor seems to understand. The problem, I think, was with the equations which, as it turns out, are images. Strangely enough, these images were visible on my post last night, but last night I was using IE on my wife's computer. Normally I use a Mac and one of four browsers (Firefox, Camino, Opera or Safari), depending on need. Or I'm on my Linux box and use Firefox. No images are visible on any of these, although the text is fine.

I finally went with the suggestion to post the doc in JPEG format. This worked, but the print is almost too fine to read. The original JPEGs that I uploaded are very legible, but CR4's image-posting mechanism squishes them down too much.

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#39

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 12:38 PM

but CR4's image-posting mechanism squishes them down too much.

I am not sure what you mean by "squishes them down", but you can manipulate (stretch horizontal or vertical, or both) any image you insert using the grips on the center of the borders or on the corners of the image after you highlight it by a right-click. At least, as long as you are still able to edit the posting.

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#40

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 1:46 PM

Hi STL,

Yes, I tried that - after my original post was closed for editing (wouldn't you know it!). I opened a new 'reply' window, uploaded the images and tried resizing them that way, but without actually posting them (I've cluttered up this thread enough as it is). CR4 reduces the image resolution before posting and so using the grips to enlarge the image after the fact makes the details larger but more fuzzy. But it did help somewhat even so; especially where the tiny subscripts were concerned.

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#52

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 1:53 AM

I'm on Windows XP and use IE 7.0, and all your equations were placeholders. Then again, I've known placeholders to suddenly show the correct image. However, they are right about OS's, but it's even more restraining... Word makes equations one thing, while FrameMaker in the same OS uses something else to display equations. Each software program pretty much has their own way of doing things.

Even when one uses RTF to cut & paste from one program into another it doesn't always work. I sent the contents of an article from a web page to another CR 4'er through PM. While the article got through, the images didn't, not even placeholders; and I cut and pasted HTML.

Will we ever have a REAL standard? Probably not - car have been around forever, and you still can't swap parts without a lot of hacking.

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#23

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 6:31 AM

Haven't looked at other postings yet, but I would say λo = h.c/(E.d.e) where

h = Planck's constant 6.63.10-34 J.s

c = velocity of light, 3.108 m/s

E = electric field, volt/m

d = distance, m

e = electronic charge, 1.6.10-19 coulomb.

Only ones we can pick are E and d, and trying E = 104 volt/m, and d = 0.1 m gives

λo = 1.24.10-9 m = 1.24 nm. Light is from ~ 450 - 700 nm so doesn't sound unreasonable.

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#36

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 11:33 AM

Hi Codemaster,

You will need to accommodate the metal plate's work function in your computations; ie, the energy required to dislodge an electron from the metal constituting the plate. Different metals have different work functions. Cesium's is 2.1 eV, while platinum is at the other end of the scale at 6.2 eV (that's why cesium was used in early vacuum photodiodes).

As the energy of the incident photon in the Challenge is greater than the metal's work function (as it has to be for an electron able to traverse distance d), the balance of the energy manifests as the kinetic energy of the ejected electron.

Work function: φ = hf0 = hc/λ0

Energy of incident photon: hf = hc/λ

Kinetic energy of ejected electron: Ek = mev2/2,

And so

Ek = hc/λ - hc/λ0 = mev2/2

The ejected electron's initial kinetic energy is such that the electron starts out at v and decelerates where it is just able to reach d. As the retarding voltage is known (but not stated), and the electron's rest mass, charge and the distance it travels in a uniform electric field are all known, we can compute the electron's kinetic energy. This energy corresponds to the difference between the energy of the incident photon, whose wavelength λ is known, and the energy required to eject an electron from the metal, which is unknown but which determines d. Solving for this difference in terms of d and λ gives us the energy of the work function which, in turn, determines the wavelength of the photon whose energy is equal to the work function. Ie, λ0.

We don't know v, but we can derive it by knowing how much force is exerted on an electron in a uniform electric field of strength Ef:

Fe = Efqe, where

Fe = the force on the electron, in Newtons

Ef = the electric field strength, in Newtons/Coulomb

qe = the charge of an elecron, in Coulombs

We also know that

Fe = mev2/2 where

me = rest mass of an electron.

From these we can determine (and eliminate) v, ultimately leading to an expression for λ0...

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#37

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 12:19 PM

Correction: Fe = mea (force), not Fe = mev2/2 (energy)

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#38

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 12:35 PM

OK Europium, thanks, I just did a quick calculation equating the energy of the photon to that needed to move the electron through an electric field. Seems that's not the whole story.

Codey

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#71

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 10:23 PM

Hi Europium,

I agree with your final answer, however provide a simpler route which doesn't have to include and then eliminate the kinetic energy and velocity etc.

Work function (energy) = φ = hc/λ0

Incident photon energy = hc/λ

Therefore the energy of ejected electron = hc/λ - hc/λ0

The retarding force as has been stated F = E.q (Newtons)

(E= electric field in Newtons/Coulomb, q = charge of electron in Coulombs)

Work (or energy) can be described as Force x distance (in Newton metres), therefore the energy retarding the electron can be given as:

Retarding energy = E.q.d

Balancing the retarding energy with the ejected electron energy we have

E.q.d = hc/λ - hc/λ0

or hc/λ = hc/λ0 + E.q.d

Then following the solving from post #30 we are left with

λ0 = hcλ/(hc-Eqdλ)

NB. Without the work function (as previous answers λ0 = hc/(Eqd) ) and if the electric field was zero, λ0 would become infinite corresponding to a photon with zero energy (no photon?). Would electrons then be sponaneously emitted to any value of d?

TJS

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#27

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 7:55 AM

I wonder if you could build a Star Trek variety deflector array with this concept. I bet somebody in the world is experimenting with the idea. Let's hear from the physicists out there!

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#32

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/13/2007 10:41 AM

Rick speculates: "I wonder if you could build a Star Trek variety deflector array..."

-----

Why on earth would you want to deflect variety?

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#55

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 4:55 AM

The electrons are ejected a distance d. So they're d-ejected. Sad but true.

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#61

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/14/2007 12:09 PM

That's d-pressing. You're d-ismissed.

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#74

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 1:20 AM

I'll go sit quietly facing the corner. ( Believe that and your madder than I am )

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#77

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 4:21 AM

That's all getting rather d-Ishmael
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#80

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 11:05 AM

I'm going to dirac laughing some day.

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#81

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 11:11 AM

....yes, I can be a little bit of a planck at times.

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#83

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 11:34 AM

Yes, you certainly can. Sometimes I just wanna kick your mass!

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#84

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 11:47 AM

Oh, just shut your ∏ hole!

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#85

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 1:05 PM

Why? Afraid I might talk circles around you, you uncircumscribed heathen? Hehe

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#86

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 2:44 PM

g, come and Avogadro if you think you're hard enough* ! Kris and STL have constant humour, we can all see what you amount to ! I feel faintly nauseous realizing that a little bit of you is in me !

* This invitation is often heard near Brit football crowds.

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#87

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 4:44 PM

What is the cause of this degeneration? Surely a rare-earty with no known biological role and a STLactite can survive the punitentary without rebating nutkin (or vice versa, of course)

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#90

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 1:09 AM

Rebating Nutkin ! Groovy. I do tend to rabbit...

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#89

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/15/2007 10:47 PM

Here are a few notes about the biological role of europium.

Europium has no biological role.

-----

<sigh> Thank goodness!

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#91

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 1:24 AM

I just found out about europium nanorods. It sounds like Europium may have a biological role ! As for myself..... FYZ is apparently a Trojan, though I refuse to believe that STL is anything to do with Standard Template Library.

< idiotic trivia mode off >

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#93

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 5:15 AM

Neither a trojan nor a virus, though I have been described as a worm (though more commonly as a toad, which I think makes me a self-consuming cannibal).

Biologically, Eu would behave as a substitutional ion for Ca, but given its atomic weight, it is unlikely to be organically desirable in any quantity

In the case you cite, its use is as a synthetic marker, and the nano-rod wraps it up so that the Europium itself is not biologically active.

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#94

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 6:46 AM

That almost sounds like admitting to being a nematode. Even more horrendous, is that it sounds similar in form to Eu's nanorod !

This is early in the day for even me to get myself into such a diabolical interpretation. The weekend is nearly upon us, so there is yet time for me to dig myself into a deeper hole than normal. Discovering that I'm some sort of warped blade has sent me downhill rapidly. If only I had read more about particle physics, I could add something useful to the discussion. To make amends I shall read your current mini-discussion with vermin with full interest.

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#95

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 7:15 AM

From your link "We haven't seen any evidence of human particles yet, though." At last, a rational explanation of dark matter. Or perhaps it isn't humans, but your alternate avatar?

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#96

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 7:54 AM

Shhh, I'm trying to figure out what matters here. 'N' I don't want to get into heavy water !

<pst - do I sound like I know what I'm talking about ? >

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#97

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 9:19 AM

Hey Kris,

I don't know where you found this picture, but it sure looks like a neutrino detector. If so you don't have to worry about getting into heavy water, just very pure ordinary water. Besides, you're in enough hot water as it is...

Those studs (relax: you're not one of them ) covering the surface are photomultipliers - light detectors sensitive enough to see individual photons.

On the other hand (I have five fingers) it could be a giant, high-tech nut that you buried last year and forgot...

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#98

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 9:58 AM

Yes, it does look rather like a Neutrino detector. But I don't think it looks much like Kamiokande or Sudbury.

Incidentally, I believe Sudbury uses heavy water with an outer screen of 'ordinary' ultra-pure water. I suppose that whether you use ordinary or heavy water depends on the trade-off between sensitivity and discrimination?

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#100

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 10:15 AM

Hey, have I confused you guys ! 'Guess that thing in one' - it isn't the 'Dark Star' off of star wars. ROFL.

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#109

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 12:26 PM

I said it didn't appear to be either of the neutrino detectors that I've seen. It's below ground and the same basic shape, but looks rather crudely made by comparison. Pop for a propular film? Police elucidate (if you believe that...).

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#116

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 3:08 PM

OOOOh !. Now, I'm not going to tell. I challenge all : what is that thing and where is it. For the insane, what does it do, why does it do it, how does it do it, and will we ever known if it does it. Papers in by next Tuesday Please. Marks will be awarded for showing the calculations. All submissions must carry the statement " All rights assigned to KrisDel Products Ltd" and carry a valid signature. If they don't, those rights are assumed anyway. Usual terms and conditions etc...

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#120

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 5:30 PM

So it's a real scientific instrument, but the photographer didn't glam it up like the pictures I've seen from Kamiokande and Sudbury. Sphere looks brown rather than silver, unplated copper or what? Given your earlier clue about heavy-water, I've no idea what it might be if not a detector for penetrative particles. Even if that is right, I've no idea at all beyond that. Europium - if we believe Dagger (curious - previously I always started the word with different first two letters when people were not being cooperative) that it's not a neutrino detector, have you any ideas?

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#122

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 5:42 PM

Keep trying ! It's real, and it's there.

Clue : it's not a film set.

Annoyance factor : there are more, but I can't tell you about them ( This sounds like a conspiracy theory, but honest, I can't ) !

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#99

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 10:10 AM

...and Albania wants me to buy an air force, but I haven't done it.Yet ! Calling it other than the Confederate Air Force is just playing up to folk.

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#101

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 10:22 AM

The standard US Kit Kat is milk chocolate covered wafers, usually 4 sticks to a bar (about 4 inches long), each stick about 1/2 inch wide. However, Kit Kat minis are available, usually around Halloween to give out to the Trick-or-Treaters. These are usually about half the length, a little narrower and only two sticks.

This year my wife bought some "special" Halloween Kit Kat minis that were orange color. I tried one and was highly disappointed. I was expecting something like a Cadbury Orange with Orange flavored milk chocolate. No orange flavor. No chocolate flavor either, just a sweet and creamy crunch, tasting like so-called "white chocolate".

I think they missed the boat on that one.

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#102

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 10:41 AM

I should have known that you would eventually appear ! Just by odd coincidence I saw a 20 min documentary series yesterday devoted to 'Classic British Brands' ( I think it was channel 4). The episode I saw was devoted to 'Kit Kat'. The variations around the world were amazing. It's history during war years was also great. The site I linked didn't do it justice - it's completely iconic. It has, at times, had a blue and also a green wrapper(currently red). It's success seems to have been driven by both innovative packaging (foil within paper) and also advertising ( " Have a break, have a Kit Kat). The name is completely lost in the mystery of time, though it probably harks back to the 'Kit-Kat clubs' that existed in the early 20's ( riotous clubs of blokes, as far as I know). Like other brands such as 'coke' they have tried to experiment at times, but failed miserably. It proves the old adage 'if it ain't broke, don't fix it'.

Personally I never buy them ! They're OK, but 'Mars Bar' is a more usual Brit snack bar.

I have not the faintest idea ,or excuse, for how I came to discuss this within this thread. It is sort of interesting though.

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#108

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 12:19 PM

Presumably you liked their jingle, which I prefered to hear as follows
"A Mars a day helps your teeth rot away"

Personally, I might just manage to eat a Kit-kat if the covering was entirely converted to dark chocolate and they removed the sugar from the biscuit...

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#110

### Re: Ejected Electrons: Newsletter Challenge (11/06/07)

11/16/2007 1:11 PM

<crooning with a raspy baritone>

"Give me a break, give me break, break me off a piece if that Kit Kat bar!"

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