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A source $\mathrm{S}_1$ is producing, $10^{15}$ photons/s of wavelength $5000 Å$. Another source $S_2$ is producing $1.02 \times 10^{15}$ photons per second of wavelength $5100 Å$. Then, (power of $\left.S_2\right) /\left(\right.$ power of $S_1$ ) is equal to
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The correct answer is:
1.00
Number of photons emitted per second
$$
\begin{array}{cc}
\quad \mathrm{n}=\frac{\mathrm{P}}{\left(\frac{\mathrm{hc}}{\lambda}\right)} \\
\therefore \quad \mathrm{P}=\frac{\mathrm{nhc}}{\lambda} \\
\Rightarrow \frac{\mathrm{P}_2}{\mathrm{P}_1}=\frac{\mathrm{n}_2 \lambda_1}{\mathrm{n}_1 \lambda_2}=\frac{1.02 \times 10^{15} \times 5000}{10^{15} \times 5100}=1
\end{array}
$$
$$
\begin{array}{cc}
\quad \mathrm{n}=\frac{\mathrm{P}}{\left(\frac{\mathrm{hc}}{\lambda}\right)} \\
\therefore \quad \mathrm{P}=\frac{\mathrm{nhc}}{\lambda} \\
\Rightarrow \frac{\mathrm{P}_2}{\mathrm{P}_1}=\frac{\mathrm{n}_2 \lambda_1}{\mathrm{n}_1 \lambda_2}=\frac{1.02 \times 10^{15} \times 5000}{10^{15} \times 5100}=1
\end{array}
$$
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