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Monochromatic light of wavelength $667 \,\,nm$ is produced by a helium neon laser. The power emitted is $9 \,\,mW.$ The number of photons arriving per sec. on the average at a target irradiated by this beam is
$3 \times 10^{16}$
$9 \times 10^{15}$
$3 \times 10^{19}$
$9 \times 10^{17}$
Solution
$\lambda = 6670\mathop {\,{\text{A}}}\limits^o $
$E$ of a photon $ = \frac{{12400\,\,{\text{eV}}\mathop {\text{A}}\limits^o }}{{6670\mathop {\,{\text{A}}}\limits^o }}$ $ = \frac{{12400}}{{6670}} \times 1.6 \times {10^{ – 19}}{\text{J}}$
Energy emitted per second, power $P=9 \times 10^{-3}\, \mathrm{J}$
$\therefore$ Number of photons incident $=\frac{\text { Power }}{\text { Energy }}=\frac{P}{E}$
$ = \frac{{9 \times {{10}^{ – 3}} \times 6670}}{{12400 \times 1.6 \times {{10}^{ – 19}}}}$ $ = 3 \times {10^{16}}$
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