A source `S_(1)` is producing `10^(15)` photons per second of wavelength `5000Ã…`. Another source `S_(2)` is producing `1.02xx10^(15)`
Then, `("Power of" S_(2))//("Power of"S_(1))` is equal to

Options

A. `1.00`
B. 1.02
C. 1.04
D. 0.98

Answer

A

Explanation

(a) : For a source `S_(1)`, Wavelength, `lamda_(1)=5000Ã…`
Number of photons emitted per second, `N_(1)=10^(15)`
Energy of each photon, `E_(1)=(hc)/(lamda_(1))`
Power of source `S_(1),P_(1)=E_(1)N_(1)=(N_(1)hc)/(lamda_(1))`
For a source `S_(2)`, Wavelength, `lamda_(2)=5100Ã…`
Number of photons emitted per second, `N_(2)=1.02xx10^(15)`
Energy of each photon, `E_(2)=(hc)/(lamda_(2))`
Power of source `S_(2),P_(2)=N_(2)E_(2)=(N_(2)hc)/(lamda_(2))`
`:.("Power of "S_(2))/("Power of "S_(1))=(P_(2))/(P_(1))=(lamda_(2))/((N_(1)hc)/lamda_(1))=(N_(2)lamda_(1))/(N_(1)lamda_(2))`
`=((1.02xx10^(15)"photons"//s)xx(5000xx10^(-10)))/((10^(15)"photons"//s)xx(5100xx10^(-10)))=(51)/(51)=1`