The ratio of the power of a light source \(S_1\) to that the light source \(S_2\) is \(2 . S_1\) is emitting \(2 \times 10^{15}\) photons per second at 600 nm . If the wavelength of the source \(S_2\) is 300 nm , then the number of photons per second emitted by \(S_2\) is _______ \(\times 10^{14}\).

Since power emitting by a source is given as
\(\begin{aligned}
& =\frac{\text { Total energy emitted }}{\text { time }} \\
& =\frac{\left(E_1 \text { photon }\right) \times \text { Number of photons }(N)}{t} \\
& P_1=\left(E_1\right) n
\end{aligned}\)
\(\begin{aligned}
& \frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{\left(\mathrm{E}_1\right) \mathrm{n}_1}{\left(\mathrm{E}_2\right) \mathrm{n}_2}=\frac{\left(\frac{\mathrm{hC}}{\lambda_1}\right) \mathrm{n}_1}{\left(\frac{\mathrm{hC}}{\lambda_2}\right) \mathrm{n}_2} \\
& \frac{\mathrm{P}_1}{\mathrm{P}_2}=\left(\frac{\lambda_2}{\lambda_1}\right) \frac{\mathrm{n}_1}{\mathrm{n}_2}
\end{aligned}\)
Substituting the given values
\(\begin{aligned}
& 2=\left(\frac{300}{600}\right) \times \frac{2 \times 10^{15}}{\mathrm{n}_2} \\
& \mathrm{n}_2=\frac{1}{2} \times 10^{15}=5 \times 10^{14} \text { Photon } / \mathrm{sec}
\end{aligned}\)