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The energy of a photon of light with wavelength $5000\,\mathop A\limits^o $ is approximately $2.5\, eV$. This way the energy of an $X-$ ray photon with wavelength $1\,\mathop A\limits^o $ would be
$\frac{{2.5}}{{{{\left( {5000} \right)}^2}}}\,eV$
$2.5\times5000\, eV$
$\frac{{2.5}}{{{{\left( {5000} \right)}^2}}}\,eV$
$\frac{{2.5}}{{5000}}\,eV$
Solution
Energy of photon
$E=\frac{h c}{\lambda}$
$ \Rightarrow \quad 2.5{\rm{eV}} = \frac{{{\rm{hc}}}}{{5000 \times {{10}^{ – 10}}}}$ (as $\lambda = 5000$ $\mathop {\rm{A}}\limits^o $)
$\Rightarrow \mathrm{hc}=2.5 \times 5 \times 10^{-7} \mathrm{\,eV}$
For $\mathrm{X}-$ ray photon, $\mathrm{c}=$ same, $\mathrm{h}=$ constant
$\Rightarrow \mathrm{E}=\frac{\mathrm{hc}}{\lambda_{\mathrm{x}-\mathrm{ray}}}$
$=\frac{2.5 \times 5 \times 10^{-7}}{1 \times 10^{-10}} \mathrm{eV}$
$=2.5 \times 5000 \mathrm{\,eV}$
