Question

Estimate the ratio of shortest wavelength of radio waves to the longest wavelength of gamma waves.

Hint:

The ratio of wavelengths in different types of electromagnetic waves can vary widely, with radio waves having much longer wavelengths than gamma rays.

Answer 1

The wavelength \( \lambda \) of an electromagnetic wave is related to its frequency \( \nu \) and the speed of light \( c \) by the equation: \[ \lambda = \frac{c}{\nu} \] 
- The longest wavelength of gamma rays is typically around \( 10^{-12} \, \text{m} \) and the shortest wavelength of radio waves is around \( 10^2 \, \text{m} \). 
Therefore, the ratio of the shortest wavelength of radio waves to the longest wavelength of gamma rays is: \[ \text{Ratio} = \frac{10^2}{10^{-12}} = 10^{14} \] Thus, the ratio is \( 10^{14} \).