Question

Calculate the wavelength of an X-ray whose frequency is $1.0\times {{10}^{18}}Hz$
$\left( a \right)3.3\times {{10}^{-11}}m$
$\left( b \right)3.0\times {{10}^{-10}}m$
$\left( c \right)3.3\times {{10}^{-9}}m$
$\left( d \right)3.0\times {{10}^{-8}}m$
$\left( e \right)3.0\times {{10}^{26}}m$

Answer 1

Hint: Since, there is a direct value of frequency given to us of an X-ray so, we will apply the formula of wavelength and with the substitution of value of speed in light we will solve the numerical to get the value of wavelength. As the frequency is in Hz but the wavelength is going to be in meters.

Formula used:
$\lambda =\dfrac{c}{f}$, where c is speed of light, f is frequency and $\lambda $ is a wavelength, $c=3\times {{10}^{8}}m/s$.

Complete answer:

A. Wavelength: We define wavelength as the length of the wave which is measured by finding distance between two crests or troughs of a wave. As the wave is in the form of a wavy type in structure, the crest is basically the top point of the wave which corresponds like a hill. On the other hand, the trough is the lowest point of the wave which resembles the depth created between two hills. We can calculate waves by dividing the speed of light (which is in the form of wave) by the frequency of the wave. This is numerically written as $\lambda =\dfrac{c}{f}$.

B. Frequency: We say that frequency is the measure of the number of occurrences of any form of light which is repeated in a certain interval of time. Since, we are using frequency for waves, so it is a number of waves repeating per unit time.

As in the question, we are given an X-ray which is with a frequency is $1.0\times {{10}^{18}}Hz$ so, we can find wavelength of it by using formula $\lambda =\dfrac{c}{f}$ and $c=3\times {{10}^{8}}m/s$, we get
 $\begin{align}
  & \lambda =\dfrac{3\times {{10}^{8}}m/s}{1\times {{10}^{18}}Hz} \\
 & \Rightarrow \lambda =\dfrac{3m/s}{1\times {{10}^{10}}Hz} \\
 & \Rightarrow \lambda =3\times {{10}^{-10}}m \\
\end{align}$

So, the correct answer is “Option B”.

Note:
While solving the numerical we will check for the units before solving because if the units are in correct form then we will get the wrong answer. After the step $\lambda =\dfrac{3m/s}{1\times {{10}^{10}}Hz}$ we have converted directly the value of wavelength in meters. But actually this is done due to the fact that $Hz=\dfrac{1}{s}$ after which seconds get cancelled and the leftover unit which is meters comes forward for defining wavelength. By remembering these points while solving such numerical will lead towards the right answer.