Question

The wavelength of an X-ray beam is $10\AA$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\left(\raisebox{1ex}{$xh$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)$ kg. The value of $x$ is _______.

Answer 1

Step 1: Given data:-

The wavelength of an X-ray beam = $10\AA$

The mass of a fictitious particle having the same energy as that of the X-ray photons is $(\raisebox{1ex}{$xh$}\!\left/ \!\raisebox{-1ex}{$3)$}\right.$ kg.

We need to find the value of x.

Step 2:- Calculating the value of x

$E=\raisebox{1ex}{$hc$}\!\left/ \!\raisebox{-1ex}{$\lambda =m{c}^2$}\right.$

$m=\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$c\lambda $}\right.$ will be the mass of a particle having the same energy.

Now, according to the question

$(\raisebox{1ex}{$xh$}\!\left/ \!\raisebox{-1ex}{$3)$}\right.=\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$c\lambda $}\right.$

$x=3/c\lambda$

$x=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$3\times {10}^8\times 10\times {10}^{-10}$}\right.$

$x=10$

Hence, the value of $x$ is $10$.