JEE Main 2025 — 24 January, Evening Shift — Question 66

Since power emitting by a source is given as

$=\frac{\text { Total energy emitted }}{\text { time }}$

$=\frac{\left(\mathrm{E}_{1} \text { photon }\right) \times \text { Number of photons }(\mathrm{N})}{\mathrm{t}}$

$P_{1}=\left(E_{1}\right) n$

$\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\frac{\left(\mathrm{E}_{1}\right) \mathrm{n}_{1}}{\left(\mathrm{E}_{2}\right) \mathrm{n}_{2}}=\frac{\left(\frac{\mathrm{hC}}{\lambda_{1}}\right) \mathrm{n}_{1}}{\left(\frac{\mathrm{hC}}{\lambda_{2}}\right) \mathrm{n}_{2}}$

$\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\left(\frac{\lambda_{2}}{\lambda_{1}}\right) \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}$

Substituting the given values

$2=\left(\frac{300}{600}\right) \times \frac{2 \times 10^{15}}{\mathrm{n}_{2}}$

$\mathrm{n}_{2}=\frac{1}{2} \times 10^{15}=5 \times 10^{14}$ Photon $/ \mathrm{sec}$