MCQ
The number of photons emitted by a monochromatic (single frequency) infrared range finder of power $1\, \mathrm{~mW}$ and wavelength of $1000 \,\mathrm{~nm}$, in $0.1$ $second$ is $\mathrm{x}\, \times 10^{13}$. The value of $\mathrm{x}$ is ..... .

(Nearest integer)

$\left(\mathrm{h}=6.63 \times 10^{-34}\, \mathrm{Js}, \mathrm{c}=3.00 \times 10^{8} \,\mathrm{~ms}^{-1}\right)$

  • $50$
  • B
    $500$
  • C
    $5$
  • D
    $663$

Answer

Correct option: A.
$50$
a
Energy emitted in $0.1\, \mathrm{sec}$.

$=0.1\, \mathrm{sec} \cdot \times 10^{-3} \,\frac{\mathrm{J}}{\mathrm{s}}$

$=10^{-4}\, \mathrm{~J}$

If $'n'$ photons of $\lambda=1000\, \mathrm{~nm}$ are emitted,

$\text { then ; } 10^{-4}=\mathrm{n} \times \frac{\mathrm{hc}}{\lambda}$

$\Rightarrow 10^{-4}=\frac{\mathrm{n} \times 6.63 \times 10^{-34} \times 3 \times 10^{8}}{1000 \times 10^{-9}}$

$\Rightarrow \mathrm{n}=5.02 \times 10^{14}=50.2 \times 10^{13}$

$\Rightarrow 50$ (nearest integer)

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