Question

De broglie waves

(Just realized I put this in math section, sorry)

Answer 1

I know the bohr radius is \[a_0 = \epsilon_0 \frac{ h^2 }{ \pi m e^2 }\]

Answer 2

@Kainui

Answer 3

Do you have any other formulas that seem related for me to play with? I'd rather not try to bring up some calculus thing again when really you're given some simpler equation haha XD

Answer 4

So electrons have to be a wavelength equal 5% of the bohr radius, the number for bohr radius is \[a_0 = 5.291 \times 10^{-11}m\]

Answer 5

I was thinking about rhydberg but then it's only for hydrogen atom, and the question is pretty generic and doesn't mention it, so I'll exclude that for now haha.

Answer 6

Ok so I just found something, the de Broglie wavelength of an electron is given by \[\lambda = \frac{ h }{ p } = \frac{ h }{ \sqrt{2meV_{ba}} }\]

Answer 7

As this is for a non relativistic particle

Answer 8

I would have to find the Voltage then mhm

Answer 9

Ok good, so now how is the momentum related to the energy?

Answer 10

Yeah looks like you're about there. I'm not really helping it seems as much as watching you haha

Answer 11

Well relativisticly \[E^2 = (pc)^2+(m_0c^2)^2\]

Answer 12

Ah wait, but I shouldn't be using relativistic until the second part of the question especially because De Broglie wavelength for an electron isn't for a relativistic particle, I think I answered the second part with just this sentence haha.

Answer 13

The broccoli waves? 0_o

Answer 14

\[p = \sqrt{2meV_{ba}}\] so to get voltage I would need the momentum first then I guess right?

Answer 15

Haha, it's pronounced "dr broy"

Answer 16

ah :) i see

Answer 17

He was the one that discovered light has a particle and wave very cool, there's a long paper he wrote you can find online with all that explanation, interesting stuff, but back to the question haha :P

Answer 18

So I'm thinking we have to unknowns, the momentum and the voltage, does that seem right?

Answer 19

Well it seems to me that the voltage and momentum are related

Answer 20

Well that's what you're solving for haha... \[\LARGE \lambda = .05a_0=\frac{h}{p}\]

Answer 21

Yeah haha, I just got that to :P

Answer 22

Well the voltage, momentum, energy are all very closely related. You can use any of them interchangeably as long as you multiply a few constants by it to get from one to the other.

Answer 23

Yes, I see.

And then we can just solve for energy using \[E = hf\]

Answer 24

Yeah often times physicists/chemists will say some confusing things like "this has energy of such and such" when really they're talking about wave numbers or frequency, and it's just because of this equation here relates them by a constant. \[\LARGE E= h \nu = hc \bar \nu\]

Answer 25

Yeah I've noticed that haha, but isn't that equation only specifically for a photon?

Answer 26

Well in any case, how do we know it's relativistic or not?

Answer 27

Depends on what your teacher says "relativistic" means. Generally speaking if the spead divided by the speed of light is really tiny, then it's considered "classical"

Answer 28

That's what I thought it would be, but I guess I'll look through the book and see if it differs in any other way, thanks a lot for your help Kainui!

Answer 29

I am actually set to start learning this stuff on Monday! I hope it's going well!

By the way, OpenStudy doesn't allow me to message you! It says that you don't accept messages.

Answer 30

That's awesome Eric, it is some interesting stuff.

Sorry about that! I fixed it, apparently it was on no one could message me haha, it's fixed now! :P
Thanks for letting me know!

Answer 31

No problem! I bet this stuff is neat! I'm not going to read this question over right now though, just because I have some other things I'm working on! For that same class, too!