Correct Answer - Option 3 : 0.5%
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:
λ = 0.250 nm, θ = 60°
\(λ ' = λ + \frac{h}{{{m_e}C}}\left( {1 - \cos \theta } \right)\)
\(λ'= 0.25 + \frac{{6.63 \times {{10}^{ - 34}}J}}{{9.11 \times {{10}^{ - 31}} \times 3 \times {{10}^8}}} \times {10^9}\left( {1 - \cos 60^\circ } \right)\)
λ' = 0.2512 nm
The fractional energy loss or fraction of energy transferred to electrons \( = \frac{{E - E'}}{E}\)
\( = \frac{{\frac{{hc}}{λ } - \frac{{hc}}{{λ '}}}}{{\frac{{hc}}{λ }}} = \frac{{λ ' - λ }}{{λ '}}\)
\(= \frac{{0.2512 - 0.250}}{{0.2512}} \times 100 = 0.47\approx0.5\% \)
