Question

A source $S_{1}$ is producing $10^{15}$ photons per second of wavelength $5000\, \mathring{A}$ Another source $S_{2 }$ is producing $1.02\times 10^{15}$ photons per second of wavelength $5100 \,\mathring{A}$ Then, (power of $S_{2})$/(power of $S_{1})$ is equal to

• A. $1.00$
• B. $1.02$
• C. $1.04$
• D. $0.98$

Answer 1

Answer: (A)

For a source $S_{1}$, Wavelength, $\lambda_{1}=5000\,\mathring{A}$
Number of photons emitted per second, $N_{1}=10^{15}$
Energy of each photon, $E_{1}=\frac{hc}{\lambda_{1}}$
Power of source $S_{1}, P_{1}=E_{1}N_{1}=\frac{N_{1}hc}{\lambda_{1}}$
For a source $S_{2}$, Wavelength, $\lambda_{2}=5100\,\mathring{A}$
Number of photons emitted per second, $N_{2}=1.02\times10^{15}$
Energy of each photon, $E_{2}=\frac{hc}{\lambda_{2}}$
Power of source $S_{2}, P_{2}=N_{2}E_{2}=\frac{N_{2}hc}{\lambda_{2}}$
$\therefore \frac{Power of S_{2}}{power of S_{1}}=\frac{P_{2}}{P_{1}}=\frac{\frac{N_{2}hc}{\lambda_{2}}}{\frac{N_{1}hc}{\lambda_{1}}}=\frac{N _{2}\lambda_{1}}{N_{1}\lambda_{2}}$
$=\frac{\left(1.02\times10^{15}photons/ s\right)\times\left(5000\times10^{-10}\right)}{\left(10^{15} photons /s\right)\times\left(5100\times10^{-10}\right)}=\frac{51}{51}=1$