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JEE Main 2008 (AIEEE) · Davisson-Germer, Uncertainty, Compton & X-Rays

Davisson-Germer, Uncertainty, Compton & X-Rays question from JEE Main 2008 (AIEEE)

Q21JEE Main 2008 · AIEEEMedium

Davisson-Germer, Uncertainty, Compton & X-Rays

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).

Figure

Electrons accelerated by potential VV are diffracted from a crystal. If d=1 A˚d = 1\text{ \AA} and i=30∘, Vi = 30^\circ,\ V should be about

(h=6.6×10−34 Js, me=9.1×10−31 kg, e=1.6×10−19 C)\left(h = 6.6 \times 10^{-34}\text{ Js},\ m_e = 9.1 \times 10^{-31}\text{ kg},\ e = 1.6 \times 10^{-19}\text{ C}\right)

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Answer: (b)

  1. From the figure, ii is measured from the normal, so the extra path for the lower plane is 2dcos⁡i2d\cos i.
  2. First-order peak: λ=2dcos⁡30∘=2×1×0.866=1.73 A˚\lambda = 2d\cos 30^\circ = 2 \times 1 \times 0.866 = 1.73\text{ \AA}
  3. For electrons, λ=h2meV=12.27V A˚\lambda = \frac{h}{\sqrt{2meV}} = \frac{12.27}{\sqrt{V}}\text{ \AA}
  4. V=12.271.73≈7.1⇒V≈50 V\sqrt{V} = \frac{12.27}{1.73} \approx 7.1 \Rightarrow V \approx 50\text{ V}
  5. So the answer is (b) 50 V.
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