An electromagnetic radiation has a photon energy of 13.2 keV. The radiation belongs to the region of
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → X-rays
The wavelength decides the region of the electromagnetic spectrum. For a photon of energy \( E \), the wavelength is \( \lambda=hc/E \), with \( h=6.63\times10^{-34}\,\mathrm{J\,s} \), \( c=3\times10^{8}\,\mathrm{m\,s^{-1}} \) and \( 1\,\mathrm{eV}=1.6\times10^{-19}\,\mathrm{J} \).
The photon energy in joules is:
\( \begin{aligned} E &= 13.2\times10^{3}\,\mathrm{eV} \\ &= 13.2\times10^{3}\times1.6\times10^{-19}\,\mathrm{J} \\ &= 2.11\times10^{-15}\,\mathrm{J} \end{aligned} \)
The wavelength is then:
\( \begin{aligned} \lambda &= \frac{hc}{E} \\ &= \frac{6.63\times10^{-34}\,\mathrm{J\,s}\times3\times10^{8}\,\mathrm{m\,s^{-1}}}{2.11\times10^{-15}\,\mathrm{J}} \\ &\approx 9.4\times10^{-11}\,\mathrm{m} \\ &= 0.094\,\mathrm{nm} \end{aligned} \)
Option (1) visible light — Incorrect. Visible light has wavelengths of about 700–400 nm. These are thousands of times longer than 0.094 nm, and its photons carry only a few eV.
Option (2) ultraviolet — Incorrect. Ultraviolet covers about 400 nm down to 0.6 nm. The value 0.094 nm is shorter than the shortest ultraviolet wavelength.
Option (3) infrared — Incorrect. Infrared lies beyond the red end of the visible spectrum. Its wavelengths are longer than about 700 nm, so its photons have even less energy than visible photons.
Option (4) X-rays — Correct. The X-ray region covers wavelengths from about 10 nm down to \( 10^{-4}\,\mathrm{nm} \). The value 0.094 nm lies inside this range.
NCERT (2026-27):
X-rays – “Beyond the UV region of the electromagnetic spectrum lies the X-ray region. … It covers wavelengths from about 10–8 m (10 nm) down to 10–13 m (10–4 nm).”