Case: Read the passage and answer the question.
The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes – the visible light that comes from a lamp in your house and the radio waves that come from a radio station are two types of electromagnetic radiation. The other types of EM radiation that make up the electromagnetic spectrum are microwaves, infrared light, ultraviolet rays, X-rays and gamma rays.
In vacuum, the ratio of the frequency of X-rays of wavelength \( 10^{-10}\,\mathrm{m} \) to the frequency of radio waves of wavelength 750 m is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 7.5\times10^{12} \)
X-rays and radio waves are both electromagnetic waves, so in vacuum they travel with the same speed \( c \). For each of them \( \nu\lambda=c \), so the frequency is inversely proportional to the wavelength.
The wavelengths are:
\( \lambda_X=10^{-10}\,\mathrm{m} \)
\( \lambda_R=750\,\mathrm{m} \)
The ratio of the frequencies is:
\( \begin{aligned} \frac{\nu_X}{\nu_R} &= \frac{c/\lambda_X}{c/\lambda_R} \\ &= \frac{\lambda_R}{\lambda_X} \\ &= \frac{750\,\mathrm{m}}{10^{-10}\,\mathrm{m}} \\ &= 7.5\times10^{12} \end{aligned} \)
Hence, the frequency of the X-rays is \( 7.5\times10^{12} \) times that of the radio waves. Both still move through vacuum at the same speed.
NCERT (2026-27):
Points to Ponder – “1. The basic difference between various types of electromagnetic waves lies in their wavelengths or frequencies since all of them travel through vacuum with the same speed.”