Correct Answer - Option 4 : 0.0074 PJ
Concept:
Compton Scattering: - It is the scattering of a photon by a charged particle usually an electron. It results in decrease in energy (or increase in wavelength) of the photon (which is usually an X-ray or gamma-ray photon).
Compton relation in given as
\({\rm{λ' }} - {\rm{λ }} = \frac{{\rm{h}}}{{{m_e}c}}\;\left( {1 - \cos \theta } \right)\)
where, λ = Initial wavelength, λ’ = Wavelength after & Scattering, h = Planck Constant, me = Electron rest mass, c = speed of light, θ = Scattering angle
\(\frac{h}{{{m_e}c}}\) is known as Compton wavelength of the electron and is equal to 2.43 × 10-12 m
Calculation:
Given:
Given
λ = 2.54 × 10-11‑ m, θ = 60°
\(\lambda ' = \lambda + \frac{h}{{{m_2}c}}(1 - \cos \theta )\)
= \(2.54 \times {10^{ - 11}} + 2.43 \times 1{ - ^{ - 12}}\left( {1 - \frac{1}{2}} \right)\)
= \(25.4 \times {10^{ - 12}} + 2.43{\rm{\;}} \times {\rm{\;}}{10^{ - 12}}{\rm{\;}} \times \frac{1}{2}{\rm{\;\;}}\)
= 25.4 × 10-12 + 1.215 × 10-12
= 26.615 pm
\(E' = \frac{{hc}}{{\lambda '}}\)
\( = \frac{{6.63\; \times \;{{10}^{ - 34}}\; \times \;3 \;\times\; {{10}^8}}}{{26.615 \;\times\; {{10}^{ - 12}}}}\)
= \(0.747 \times {10^{ - 14}} \)
= 0.0074 PJ
