The energy of X-rays with a wavelength of 1.6 | vedclass

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(C) The energy $E$ of a photon is given by $E = \frac{hc}{\lambda}$.Substituting the values: $h = 6.6 	imes 10^{-34} \, J \cdot s$,$c = 3 	imes 10^{

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(C) The energy $E$ of a photon is given by $E = \frac{hc}{\lambda}$.Substituting the values: $h = 6.6 	imes 10^{-34} \, J \cdot s$,$c = 3 	imes 10^{8} \, m/s$,and $\lambda = 1.65 	imes 10^{-10} \, m$.$E = \frac{6.6 	imes 10^{-34} 	imes 3 	imes 10^{8}}{1.65 	imes 10^{-10}} \, J$.$E = \frac{19.8 	imes 10^{-26}}{1.65 	imes 10^{-10}} \, J = 12 	imes 10^{-16} \, J$.To convert this into $eV$,divide by $1.6 	imes 10^{-19} \, J/eV$:$E = \frac{12 	imes 10^{-16}}{1.6 	imes 10^{-19}} \, eV = 7.5 	imes 10^{3} \, eV = 7.5 \, keV$.Alternatively,using the shortcut formula $E(eV) \approx \frac{12400}{\lambda(\mathring{A})}$,we get $E \approx \frac{12400}{1.65} \approx 7515 \, eV \approx 7.5 \, keV$.

The energy of $X$-rays with a wavelength of $1.65 \, \mathring{A}$ is ............. $keV$ (Given: $h = 6.6 \times 10^{-34} \, J \cdot s$,$c = 3 \times 10^{8} \, m/s$,$1 \, eV = 1.6 \times 10^{-19} \, J$). (in $.5$)

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