X-rays of wavelength of $22 p m$ are scattered from a carbon target at an angle of $85^{0}$ to the incident beam. The compton shift for X-rays is $(c o s 85^{0} = 0.088)$

2.2 p m

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1.1 p m

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0.55 p m

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4.4 p m

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Solution

The correct option is A $2.2 p m$
Compton shift is given as $Δ λ = \frac{h}{m c} (1 - c o s ϕ) = \frac{6.62 \times 10^{- 34} J s}{9.1 \times 10^{- 31} K g \times 3 \times 10^{8} m / s} (1 - c o s 85^{0})$
where $m$ is the mass of electron and $h$ is Planck's constant with $c$ as speed of light in air.
On calculation we get the shift as $Δ λ = 2.2 \times 10^{- 12} m e t e r = 2.2 p i c o m e t e r$
Option A is correct.

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