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Directions: Question No. 13 and 14 are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). 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), the de Broglie wavelength λ_dB of electrons can be calculated by the relationship (n is an integer)

1. d sin i = n λ_dB
2. 2d cos i = n λ_dB
3. 2d sin i = n λ_dB
4. d cos i = n λ_dB

Correct answer: 2d cos i = n λ_dB

Solution

Bragg's law is 2d sin(theta) = n*lambda where theta is the glancing angle measured from the plane. Since i is measured from the normal, theta = 90 - i, giving 2d sin(90 - i) = 2d cos i = n*lambda_dB.

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