Question

An X-ray tube operates at 20 kV, and a particular electron loses 5% of its kinetic energy to emit an X-ray photon at the first collision. The wavelength corresponding to this photon is

• A. 10.24 nm
• B. 6.24 nm
• C. 2.24 nm
• D. 1.24 nm

Hint:

In X-ray generation, not all the electron’s kinetic energy converts to photon energy. For precise wavelength calculations, always use the fraction of energy lost and convert the kinetic energy from eV to joules for consistency. This ensures accuracy in spectroscopic studies.

Answer 1

The Correct Option is B

The energy of the emitted photon is:
\[E = 0.05 \times \text{eV} = 0.05 \times (20 \, \text{kV})\]
Using \(E = \frac{hc}{\lambda}\), where \(h = 6.626 \times 10^{-34} \, \text{Js}\) and \(c = 3 \times 10^8 \, \text{m/s}\):
\[\lambda = \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{0.05 \times 20 \times 10^3 \times 1.602 \times 10^{-19}} \approx 6.24 \, \text{nm}\]