The first order reflection of a beam of X-rays of wavelength 1.54 Ã… from the (100) face of a crystal of the simple cubic type occurs at an angle of `11.29^(@)` . Calculate the length of the unit cell.

Options

A. `3.93 xx 10^(-4) cm`
B. `2 xx 10^(-7) cm`
C. `3.93 xx 10^(-8) cm`
D. `4.0 xx 10^8 cm`

Answer

C

Explanation

Applying bragg.s equation
` 2d sin theta = n lamda `
Given ` theta = 11.29^@ , lamda = 1.54 Å = 1.54 xx 10^(-8) cm`
n= 1
` d = (1.54 xx 10^(-8))/(2 xx sin 11.29^@) = (1.54 xx 10^(-8))/(2 xx 0.1957) = 3.93 xx 10^(-8) cm`
`d_(hkl) = (a)/(sqrt(h^2 + k^2 + l^2) = a`
` a = 3.93 xx 10^(-8) ` cm (length of the unit cell)