Question

Which is having the minimum wavelength?
(A) X-rays
(B) ultraviolet rays
(C) $\gamma - $rays
(D) cosmic rays

Answer 1

Hint: The wavelength of X-rays, $\gamma $-rays, ultraviolet rays and cosmic rays are fixed and experimentally calculated by formula
$\lambda = \dfrac{c}{f}$
Where
f $ = $ frequency of wave
c $ = $ speed of light
$\lambda = $ wavelength of wave

Complete step by step answer:
All 4 waves i.e., x-rays, $\gamma $-rays, ultraviolet rays and cosmic rays are the part of electromagnetic wave and its wavelength experimentally given as
For x-rays wavelength range is $0.01nm - 10nm$ …..(1)
For ultraviolet rays wavelength range is $400nm - 1nm$ …..(2)
For $\gamma $-rays wavelength range is Between 1 millimeter and 100 kilometers …..(3)
For cosmic rays wavelength range is ${10^{ - 14}}m$ to ${10^{ - 12}}m$ …..(4)
From equation 1, 2, 3 & 4, it is clear that cosmic rays have minimum wavelength.

So, the correct answer is “Option D”.

Note:
The wavelength order for given rays is opposite to the order of their frequencies because the frequency of the wave is inversely proportional to the wavelength.
$f \propto \dfrac{1}{\lambda }$