The frequency 1057 MHz of radiation arising from two close energy levels in hydrogen belongs to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → radio waves
The regions of the electromagnetic spectrum differ in wavelength (or frequency). So we first change the frequency to a wavelength with \( \lambda=c/\nu \), taking \( c=3\times10^{8}\,\mathrm{m\,s^{-1}} \).
\( \nu=1057\,\mathrm{MHz}=1.057\times10^{9}\,\mathrm{Hz} \)
\( \begin{aligned} \lambda &= \frac{c}{\nu} \\ &= \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{1.057\times10^{9}\,\mathrm{Hz}} \\ &\approx 0.28\,\mathrm{m} \end{aligned} \)
Option (1) radio waves — Correct. Radio waves have wavelengths greater than 0.1 m, and \( 0.28\,\mathrm{m} \) lies in this range.
Option (2) infrared waves — Incorrect. Infrared waves have wavelengths from 1 mm to 700 nm, far shorter than 0.28 m.
Option (3) ultraviolet rays — Incorrect. Ultraviolet rays have wavelengths from 400 nm to 1 nm.
Option (4) γ-rays — Incorrect. Gamma rays have the shortest wavelengths of all, below \( 10^{-3}\,\mathrm{nm} \).
NCERT (2026-27):
Electromagnetic Spectrum
