Electrons impinging on a crystal

[tanaygupta2000]

Homework Statement

Under certain conditions, a beam of electrons impinging on a crystal surface will diffract and a
scattering pattern of the beam can be obtained. What is the approximate kinetic energy of the electrons needed in order to the see the pattern?
(Assume the lattice spacing of the crystal to be 0.4 nm)
(a) 100 eV (b) 1 eV (c) 0.1 eV (d) 10 eV

Relevant Equations

Bragg's law. 2d sinθ = nλ
De-broglie wavelength, λ = h/p

Since the crystal spacing is given to be 0.4 nm, so d = 0.4 nm = 4e-10 m in Bragg's law formula
For θ = 90° & n = 1, I got λ = 2d = 8e-10 m

Using this value in De-broglie wavelength, I got p = h/λ = 8.28e-25

Now kinetic energy of the electrons is given by E = p^2/2m
Using value of p, I am getting E = 2.35 eV, which doesn't seem to match any option.
Where am I doing mistake?
Please help!

 

[TSny]

90^o is extreme. An interference pattern can be observed for n = 1 with small $\theta$.

The problem is asking for an approximate answer. The general idea is that you need $\lambda$ to be "on the order of" the lattice spacing. So, what energy do you get if you take $\lambda = 0.4$ nm?

 

[tanaygupta2000]

90^o is extreme. An interference pattern can be observed for n = 1 with small $\theta$.

The problem is asking for an approximate answer. The general idea is that you need $\lambda$ to be "on the order of" the lattice spacing. So, what energy do you get if you take $\lambda = 0.4$ nm?

p would get doubled and E would get 4 times, i.e., 4×2.35 eV = 9.4 eV ≈ 10 eV

 

[tanaygupta2000]

Thank You so much for the help !