Modern Physics Question: Davisson and Germer Expt. beam diffraction

[won0136]

Homework Statement

In the experiment of Davisson and Germer (a) show that the second- and third-orderdiffracted beams cannot occur and (b) find the angle at which the first-order diffracted beamwould occur if the accelerating potential were changed from 54 to 60 V. (c) What acceleratingpotential is needed to produce a second-order diffracted beam at 50°

I have no idea how to approach this problem...

Homework Equations

Some equations I think would come in use...:

nd=sin(theta)

The Attempt at a Solution

First off, I'm not sure what kind of answer I need to arrive and
Second, I have no idea how to approach this problem
Thank you for the help in advance!

 

[Dukon]

First I suggest you write a definition (adding it to this thread) what is a first order diffracted beam. After that, then define clearly in what second, third and higher order diffracted beams consist. Make sure these definitions are clearly presented and that they directly state necessary and sufficient conditions for each of the orders separately. Once the necessary and sufficient conditions for each order are clearly presented, then you can think whether and which any of the necessary conditions are missing for the 2nd, 3rd or any orders. That might make clear why the 2nd and 3rd orders "cannot occur" as in part "a)".

For part b) of your question, Consider that changing the voltage of the electron gun, changes the energy and momentum of the electrons. Use p=h/lambda but solve for lambda=h/p but write p as a function of voltage (you know that as voltage goes up so does p: figure out what the constant of proportionality is exactly, use the definition of 1 electron volt)

Thus using p=h/lambda, the de Broglie relation, any voltage change changes the wavelength of the electrons. Your equation provided in your number "2" is different from the one provided as the Bragg Law on the Wikipedia page for Davisson Germer: https://en.wikipedia.org/wiki/Davisson–Germer_experiment

Changing the voltage from 54 to 60V should change the expected wavelength which in turn changes the angle according to that Bragg Law equation for n=1 on that Wikipedia page.

For your part "c)" set n=2 and theta=50 and solve for lambda but use the relation between wavelength and voltage from part b) above and you should answer this "c)" question

New question, part "d)" if 2nd order diffraction is forbidden as in part "a)" why is a 2nd order diffracted beam allowed in part "c)"?

 

[won0136]

To my understanding, a first, second, or third order diffraction is the number of modes away from the zero order diffraction, which is no diffraction. To obtain a certain diffraction order, say the first, you would need some specific quantized energy, likewise with the second and third order.

b) I can assume all the potential energy given from that potential difference is converted into kinetic energy, which allows me to then use 60eV as the value for p?
this gives me a lamda = 6.893 E -17 s
Then plug into bragg's equation with n=1 since its the first order diffraction. giving a theta of = 3.20589E-16 s/nm
c) Sounds Straight forward
d) potential difference given in part C is higher than that of part A, which allowed for the diffraction of a second order diffracted beam

Thank you for your help Doug. Your questions really helped me guid myself through the process.

 

[Dukon]

You need to think more about units. Your "eV as value for p" is invalid since eV are units of energy not momentum, the units of lambda need to be in distance. This is called "dimensional analysis" so you need to make sure the dimensions of all your quantities are correct before your results make physical sense.