Question

A source $S_{1}$is producing $10^{15}$photons per second of wavelength 5000Å. Another source$S_{2}$is producing $1.02 \times 10^{15}$Photons per second of wavelength 5100Å. 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)

1.00

Answer 2

: for a source $S_{1}$

Wavelength $\lambda_{1} = 5000Å$

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 $\lambda_{2} = 5100Å$

Number of photons emitted per second $N_{2} = 1.02 \times 10^{15}$

Energy of each photon,$E_{2} = \frac{hc}{\lambda_{2}}$

Power of source $S_{2},$

$p_{2} = E_{2}N_{2} = \frac{N_{2}hc}{\lambda_{2}}$

$\therefore\frac{powerofS_{2}}{powerofS_{1}} = \frac{p_{2}}{p_{1}} = \frac{N_{2}hc}{\frac{\lambda_{2}}{\frac{N_{1}hc}{\lambda_{1}}}} = \frac{N_{2}\lambda_{1}}{N_{1}\lambda_{2}}$

$= \frac{(1.02 \times 10^{15}photons/s) \times (5000 \times 10^{- 10})}{(10^{15}photons/s) \times (5100 \times 10^{- 10})} = \frac{51}{51} = 1$