Question

The wavelength of a photon is $1.4\dot{\text{A}}$. It collides with a stationary electron. The energy of the scattered electron is $4.6\times {10}^{-16}\text{J}$. Find the wavelength of photon after collision. (Given: $h=6.63\times {10}^{-34}\text{Js})$

• A. $2.0\dot{A}$
• B. $3.2\dot{A}$
• C. $5.6\dot{A}$
• D. $1.4\dot{A}$

Answer 1

The correct option is A $2.0\dot{A}$

Initial wavelength of photon ${\lambda }_1=1.4\dot{A}$

According to the law of conservation of energy,

Loss in energy of the photon = Gain in energy of the electron

$\Rightarrow E_1-E_2=4.26\times {10}^{-16}$

$\Rightarrow \frac{hc}{{\lambda }_1}-\frac{hc}{{\lambda }_2}=4.26\times {10}^{-16}$

$\Rightarrow 6.63\times {10}^{-34}\times 3\times {10}^8(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2})=4.26\times {10}^{-16}$

$\Rightarrow (\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2})=0.214\times {10}^{10}$

$\Rightarrow \frac{1}{{\lambda }_2}=\frac{1}{1.4\times {10}^{-10}}-0.214\times {10}^{10}$

$\Rightarrow \frac{1}{{\lambda }_2}=0.714\times {10}^{10}-0.214\times {10}^{10}$

$\Rightarrow {\lambda }_2=2\times {10}^{-10}\text{m}=2.0\dot{A}$

Hence, option $\left(A\right)$ is correct.