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 $10-0.1\stackrel{o}{A}$.

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 $10-0.1\stackrel{o}{A}$.
Since $1\stackrel{o}{A}={10}^{-10}m$
So, using eq. (i)
 $$\nu ={\displaystyle \frac{c}{\lambda }}={\displaystyle \frac{3\times {10}^8}{10\times {10}^{-10}}}=3\times {10}^{17}Hz$$
Also, $$\nu ={\displaystyle \frac{c}{\lambda }}={\displaystyle \frac{3\times {10}^8}{0.1\times {10}^{-10}}}=3\times {10}^{19}Hz$$
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.