Question

A photon with initial frequency ${10}^{11}Hz$ scatters off an electron at rest. Its final frequency is $0.9\times {10}^{11}Hz$. The speed of scattered electron is close to:
$(h=6.63\times {10}^{-34}Js,m_e=9.1\times {10}^{-31}kg)$

• A. $4\times {10}^{3}m{s}^{-1}$
• B. $3\times {10}^{2}m{s}^{-1}$
• C. $2\times {10}^{6}m{s}^{-1}$
• D. $30m{s}^{-1}$

Answer 1

Answer: (A)

$4\times {10}^{3}m{s}^{-1}$

Initial energy of photon $=$ Energy of photon after scattering $+$ K.E. of scattered electron

$h{v}_1=h{v}_2+\frac{1}{2}m{v}^2$

$\frac{1}{2}m{v}^2=h(v_1-v_2)$

$v^2=\frac{2h(v_1-v_2)}{m}$

$=\frac{2\times 6.63\times {10}^{-34}({10}^{11}-0.9\times {10}^{11})}{9.1\times {10}^{-31}}$

$v=\sqrt{14571428}=3.8\times {10}^3\approx 4\times {10}^{3}m{s}^{-1}$.