Question

The frequency of X-rays is of the order of
A. $3 \times {10^{18}}Hz$
B. $3 \times {10^8}Hz$
C. $3 \times {10^{10}}Hz$
D. 300Hz

Answer 1

Hint: We know that the electromagnetic spectrum is the distribution of electromagnetic radiation according to its energy. The electromagnetic spectrum in increasing order of wavelengths is Gamma, X-rays, Ultra Violet, Visible, Infrared, Microwave and Radio (GXUVIMR) and the wavelength of the X-rays range from $10 - 0.1\mathop A\limits^o $.

Formula used: Now we will apply the relation between frequency and wavelength which is $c = \nu \lambda $.
Where c is the speed of light
v is frequency
And \[\lambda \] is wavelength
So, and calculate frequency.

Complete Answer: We know that $c = 3 \times {10^8}m{s^{ - 1}}$ and also $\lambda $ ranges from $10 - 0.1\mathop A\limits^o $.
Since $1\mathop A\limits^o = {10^{ - 10}}m$
So, using eq. (i)
 \[\nu = \dfrac{c}{\lambda } = \dfrac{{3 \times {{10}^8}}}{{10 \times {{10}^{ - 10}}}} = 3 \times {10^{17}}Hz\]
Also, \[\nu = \dfrac{c}{\lambda } = \dfrac{{3 \times {{10}^8}}}{{0.1 \times {{10}^{ - 10}}}} = 3 \times {10^{19}}Hz\]
So, the Frequency of X-rays ranges from $3 \times {10^{17}}Hz$ to $3 \times {10^{19}}Hz$
Therefore, the frequency of X-rays is of the order of $3 \times {10^{18}}Hz$
Hence, option (A) is correct.

Additional Information: :
The electromagnetic spectrum in increasing order of wavelengths is Gamma, X-rays, Ultra Violet, Visible, Infrared, Microwave and Radio and can be remembered by GXUVIMR – Gandhi’s X-ray is Used Vigorously in Medical Research.

Note: We must take care of units i.e., to check whether everything is in the same units or not and also the relation between frequency and wavelength $c = \nu \lambda $. X-rays have greater frequency after Gamma rays and smaller wavelengths.