JEE Main · 2008 · 27 Apr 2008 · Offline · Modern Physics

Passage

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 in 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), de Broglie wavelength

λ_{dB}

of electrons can be calculated by the relationship (n is an integer)

(A) $d sin i = n λ_{d B}$
(B) $2 d cos i = n λ_{d B}$ ✓ Correct
(C) $2 d sin i = n λ_{d B}$
(D) $d cos i = n λ_{d B}$

Answer: (B)

Solution

The electron waves reflected from successive atomic planes interfere constructively when their path difference is a whole number of wavelengths. Here the angle

i

is measured from the normal to the planes, so the extra path travelled between reflections from two planes a distance

d

apart is

2 d cos i

. Setting this equal to an integer number of de Broglie wavelengths gives the diffraction condition

2 d cos i = n λ_{d B}

. This item carries a figure that was not captured with the question; the relation above follows from the stated geometry alone, but the missing diagram should be restored before the question is used.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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JEE Main · 2008 · 27 Apr 2008 · Offline · Modern Physics

Solution

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