Question

An $\text{X}$-ray tube operates at $20\text{kV}.$ A particular electron loses $5\%$ of its kinetic energy to emit an $\text{X}$-ray photon at the first collision. Find the wavelength corresponding to this photon.

• A. $2.56\text{nm}$
• B. $1.24\text{nm}$
• C. $3.78\text{nm}$
• D. $0.45\text{nm}$

Answer 1

The correct option is B $1.24\text{nm}$

Kinetic energy acquired by th electron in potential difference $20\text{kV}$ is

$K=20\times {10}^3\text{eV}$

The energy of the $\text{X}$- rays photon,

$E=0.05\times 20\times {10}^3\text{eV}={10}^3\text{eV}$

$\Rightarrow \frac{hc}{\lambda }={10}^3\text{eV}$

$\lambda =\frac{hc}{{10}^3\text{eV}}$

$\lambda =\frac{(4.14\times {10}^{-15}\text{eV-s})\times (3\times {10}^8\text{m/s})}{{10}^3\text{eV}}$

$\therefore \lambda =12.42\times {10}^{-10}\text{m}=1.24\text{nm}$

Hence, option $\left(\text{B}\right)$ is the right answer.