Question

If a diffraction peak is observed when electrons are incident at an angle ${}^{\prime }{i}^{\prime }$ from the normal to the crystal planes with distance ${}^{\prime }{d}^{\prime }$ between them (see figure), de-Broglie wavelength ${\lambda }_{dB}$ of electrons can be calculated by the relationship ($n$ is an integer):

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

Answer 1

The correct option is B $2d\cos i=n{\lambda }_{dB}$

From condition of constructive interference of Bragg's law,

$2dsin\theta =n{\lambda }_{db}$

but here $\theta =90-i$

So,

$2dsin(90-i)=n{\lambda }_{db}$

$\Rightarrow 2dcosi=n{\lambda }_{db}$