Question

In Davisson-Germer experiment, as shown below, where electrons are reflected from a crystal plane.


If at angle $i$, the peak diffraction is observed, the de Broglie wavelength of electrons can be calculated by

• A. $d\sin i=n{\lambda }_B$
• B. $2d\cos i=n\lambda$
• C. $2d\sin i=n\lambda$
• D. $d\cos i=n\lambda$

Answer 1

The correct option is B $2d\cos i=n\lambda$

According to Bragg's law equation,

$n\lambda =2AB+2BC$

Now, $AB=BC=\frac{d}{2}\sin \theta$

$\therefore n\lambda =2d\sin \theta =2d\cos i$


Hence, $\left(B\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question?}\\ \text{If when light is incident at a different angle of incidence, waves will interfere between 2 layers of crystal. The 2 peaks are ofset hence destructively.}\end{array}$