Question

The energy of a photon of light with wavelength $5000\stackrel{\circ }{A}$ is approximately $2.5eV$. This way the energy of an X-ray photon with wavelength $1\stackrel{\circ }{A}$ would be:

• A. $\frac{2.5}{(5000{)}^2}eV$
• B. $2.5\times 5000eV$
• C. $\frac{25}{(5000{)}^2}\cdot eV$
• D. $\frac{2.5}{5000}eV$

Answer 1

The correct option is B $2.5\times 5000eV$

Energy of photon, $E=\frac{hc}{\lambda }$
$\Rightarrow 2.5eV=\frac{hc}{5000\times {10}^{-10}}$ (as $\lambda =5000\stackrel{\circ }{A})$

$\Rightarrow hc=2.5\times 5\times {10}^{-7}eV$

For X-ray photon, $c=constant,h=constant$

$\Rightarrow E=\frac{hc}{{\lambda }_{x-ray}}$

$=\frac{2.5\times 5\times {10}^{-7}}{1\times {10}^{-10}}eV$

$=2.5\times 5000eV$

Hence, option $B$ is correct.