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, $N_2=1.02\times 10^{15}$
Energy of each photon, $E_2=\frac{hc}{{\lambda }_2}$
Power of source $S_2,P_2=N_2{E}_2=\frac{N_{2}hc}{{\lambda }_2}$
$\therefore \frac{Powerof{S}_2}{powerof{S}_1}=\frac{P_2}{P_1}=\frac{\frac{N_{2}hc}{{\lambda }_2}}{\frac{N_{1}hc}{{\lambda }_1}}=\frac{N_2{\lambda }_1}{N_1{\lambda }_2}$
$=\frac{\left(1.02\times 10^{15}photons/s\right)\times \left(5000\times 10^{-10}\right)}{\left(10^{15}photons/s\right)\times \left(5100\times 10^{-10}\right)}=\frac{51}{51}=1$