The wavelength of an X-ray beam is 10 , mathr | vedclass

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(C) The energy of an $X$-ray photon is given by $E = \frac{hc}{\lambda}$.According to the problem,the mass $m$ of a fictitious particle having the sam

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$10$

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(C) The energy of an $X$-ray photon is given by $E = \frac{hc}{\lambda}$.According to the problem,the mass $m$ of a fictitious particle having the same energy is given by $E = mc^2$.Equating the two expressions: $\frac{hc}{\lambda} = mc^2$.Solving for $m$: $m = \frac{h}{c\lambda}$.Given $\lambda = 10 \, \mathring{A} = 10 	imes 10^{-10} \, 	ext{m} = 10^{-9} \, 	ext{m}$.Substituting the value of $c = 3 	imes 10^8 \, 	ext{m/s}$:$m = \frac{h}{(3 	imes 10^8) 	imes 10^{-9}} = \frac{h}{3 	imes 10^{-1}} = \frac{h}{0.3} = \frac{10h}{3}$.Comparing this with the given expression $\frac{x}{3} h$,we get $x = 10$.

The wavelength of an $X$-ray beam is $10 \, \mathring{A}$. The mass of a fictitious particle having the same energy as that of the $X$-ray photons is $\frac{x}{3} h \, \text{kg}$. The value of $x$ is ....... . ($h =$ Planck's constant)

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