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A source $S_1$ is producing $10^{15}$ photons per second of wavelength 5000 Å. Another source $S_2$ is producing $1.02\times10^{15}$ photons per second of wavelength 5100 Å. Then (power of $S_2$)/(power of $S_1$) is equal to
A
0.98
B
1.00
C
1.02
D
1.04
Detailed Solution
Energy of one photon: $E = \frac{hc}{\lambda}$
Power of a source = number of photons emitted per second × energy of each photon: $P = \frac{nhc}{\lambda}$
$\frac{P_2}{P_1} = \frac{n_2}{n_1}\times\frac{\lambda_1}{\lambda_2}$
$\frac{P_2}{P_1} = \frac{1.02\times10^{15}}{10^{15}}\times\frac{5000}{5100} = 1.02\times\frac{1}{1.02}$
$\frac{P_2}{P_1} = 1.00$
Power of a source = number of photons emitted per second × energy of each photon: $P = \frac{nhc}{\lambda}$
$\frac{P_2}{P_1} = \frac{n_2}{n_1}\times\frac{\lambda_1}{\lambda_2}$
$\frac{P_2}{P_1} = \frac{1.02\times10^{15}}{10^{15}}\times\frac{5000}{5100} = 1.02\times\frac{1}{1.02}$
$\frac{P_2}{P_1} = 1.00$