A blue lamp emits light of mean wavelength $4500 Å$. The lamp is rated at 150 W and $8 \%$ efficiency. Then…

A blue lamp emits light of mean wavelength $4500 Å$. The lamp is rated at 150 W and $8 \%$ efficiency. Then the number of photons are emitted by the lamp per second
  1. $27.17 \times 10^{18}$
  2. $17.17 \times 10^{18}$
  3. $27.17 \times 10^{15}$
  4. $54 \times 10^{16}$

Solution

$\lambda=4500 \mathrm{~A}^{\circ}, \mathrm{P}=150 \mathrm{~W}, \eta=8 \%$
Efficiency of the lamp, $\eta=\frac{\text { Energy of photon }}{\text { Rated energy of lamp }}=\frac{\left(\frac{\mathrm{nhc}}{\lambda}\right)}{\mathrm{p} . \mathrm{t}}$ $\therefore \quad$ Number of photons emitted per second. $\begin{aligned} & \frac{\mathrm{n}}{\mathrm{t}}=\frac{\mathrm{p} . \lambda . \eta}{\mathrm{hc}}=\frac{150 \times 4500 \times \frac{8}{100}}{1240 \times 1.6 \times 10^{-19}} \\ & =27.17 \times 10^{18} \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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