KE of Electrons to give same theta as light in double slit diffraction

[Silly Sausage]

Homework Statement

Coherent light is passed through two narrow slits whose separation is d. The second-order bright fringe in the interference pattern is located at an angle of theta.

If electrons are used instead of light, what must the kinetic energy of the electrons be if they are to produce an interference pattern for which the second-order maximum is also at theta?

Homework Equations

No relevant equations givven

The Attempt at a Solution

Well, I started by saying that the wavelength of the electrons will be the same as the wavelength of light, and thought of using h=p lambda and then E=hf.

However I then confused myself because for h=p lamba I need the momentum and for that I need the speed. E=hf will give me kinetic energy wouldn't it? Can I please have some hints and pointers as to what direction I should be thinking in?

 

[Doc Al]

Well, I started by saying that the wavelength of the electrons will be the same as the wavelength of light, and thought of using h=p lambda

Good. Use that to find the momentum of the electrons.

and then E=hf.

That would apply for photons, not electrons.

How does momentum relate to kinetic energy?

 

[Silly Sausage]

OK. I used Ek = p^2/(2m) and h=p lambda

to give Ek= h^2/(lambda^2*2m)

now do I use n lmbda = dsin theta?

 

[Silly Sausage]

done it! thanks guys!

 

[Doc Al]

Sounds good to me.