Question

What is the frequency of X-rays if its wavelength is $ 0.01\dot \Lambda $ ?
(A) $ 1 \times {10^{20}}Hz $
(B) $ 3 \times {10^{20}}Hz $
(C) $ 3 \times {10^{18}}Hz $
(D) $ 1 \times {10^{18}}Hz $

Answer 1

Hint
As we already know, the speed of light is equal to the speed of X-rays. So, the speed of X-rays will be $ 3 \times {10^8}m/s $ . Then, we will convert the angstrom to metre by multiplying it by $ {10^{ - 10}} $ .
Then, use the expression and put the values in it-
 $ v = f\lambda $
where, $ v $ is the speed of X-rays,
 $ f $ is the frequency of X-rays and,
 $ \lambda $ is the wavelength of X-rays.

Complete step by step solution
The range of all types of the electromagnetic radiation is called the electromagnetic spectrum. The energy which travels and spreads out is called radiation. There are many other electromagnetic radiations which make up the electromagnetic spectrum are:
-Radio waves
-Microwaves
-Infrared rays
-Visible rays
-Ultraviolet rays
-Gamma rays
-X rays
X-rays are also a part of the electromagnetic spectrum. So, the speed of X-rays will be $ 3 \times {10^8}m/s $ because all waves which are part of the electromagnetic spectrum travel with the same speed. They travel at the speed of light. So, all the rays have a speed of $ 3 \times {10^8}m/s $ .
According to question, it is given that
Wavelength, $ \lambda = 0.01\dot \Lambda $
To convert wavelength into meters we have to multiply it by $ {10^{ - 10}} $ .
Therefore, $ \lambda = 0.01 \times {10^{ - 10}}m $
Speed of X-rays, $ v = 3 \times {10^8}m/s $
We know that, $ v = f\lambda $
 $ \therefore f = \dfrac{v}{\lambda } $
Putting the values of speed of X-rays and wavelength in the above equation, we get
 $ f = \dfrac{{3 \times {{10}^8}m/s}}{{0.01 \times {{10}^{ - 10}}m}} $
By further solving, we get
 $ f = 3 \times {10^{20}}Hz $
Therefore, we got the frequency for the X-ray.

So, the answer (B) is correct.

Note
X-ray is one form of electromagnetic radiation. Most X-rays have a wavelength ranging from $ 0.01 $ to $ 10nm $ , corresponding to frequencies in the range of 30 petahertz to 30 exahertz $ (3 \times {10^{16}}Hz $ to $ 3 \times {10^{20}}Hz) $ and energies in the range $ 100eV $ to $ 100keV. $