Question

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

A
dsini=nλdB
B
dcosi=nλdB
C
2dsini=nλdB
D
2dcosi=nλdB

Solution

The correct option is D $$2d cos \,i= n\lambda_{dB}$$From Bragg's law,  $$2d\sin\theta=n\lambda_{dB}$$or $$2d\sin(90-i)=n\lambda_{dB}$$or $$2d\cos i=n\lambda_{dB}$$So option D is correct. PhysicsNCERTStandard XII

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