Question

An X-ray tube operates at 10 keV. A particular electron loses 4 % of its kinetic energy to emit an X-ray photon at the first collision. Find the wavelength corresponding to this photon.
1. 3.1 nm
2. 1.24 nm
3. 4 nm
4. 1.6 nm

Answer 1

Correct Answer - Option 1 : 3.1 nm

Kinetic energy acquired by the electron is 10keV = 10 × 10³ eV

The energy of the photon = 0.04 × 10 × 10³ eV

Thus \(\frac{{hc}}{\lambda } = 400 \Rightarrow \lambda = \frac{{hc}}{{{{10}^3}eV}} = \frac{{4.14 \times {{10}^{ - 15}} \times 3 \times {{10}^8}}}{{400}} = \frac{{1242eV - nm}}{{400\;eV}} = 3.105\;nm\;\)