Crystal spacing of a solid surface, Bragg's law

[1101]

Homework Statement

In a particular Low Energy Electron Diffraction (LEED) study of a solid surface, electrons at 45 eV were diffracted at \phi = 53 degrees. Calculate the crystal spacing d.

Homework Equations

n\lambda=2dsin(\phi)
\lambda = hc/E
wavelength = c/v
E = vh(n + 1/2)

Note here v is the frequency (nu looked weird on this site)

The Attempt at a Solution

This questions comes from a problem in my textbook that was a recommended practice problem for an upcoming exam. Despite being an odd numbered problem the answer to it wasn't in the back of the book (figures). Anyways I just wanted to make sure I was solving it correctly.

Firstly I converted the 45 electronvolts into 7.209765E^-18 Joules
Then by wavelength = hc/E, i found the wavelength to be 2.754E^-8 Meters
Then I found the frequency to be 1.089324619E¹⁶ s^-1
Next I found n to be 1/2 (which is weird cause I thought it would be an integer)
Lastly I plugged these values into bragg's law and got 8.623E^-9 Meters

Like I said the answer was not in the book for some reason and I'd like to know if I'm doing this right

 

[nickjer]

You need to show your steps better. Also, why are you using the last equation listed? That is for a quantum harmonic oscillator. In this case you just have diffraction.