A source `S_(1)` is producing `10^(15)` photons/s of wavelength `5000 Å` Another source `S_(2)` is producing `1.02 xx 10^(15)` photons per second of wavelength `5100 Å`. 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

For a source `S_1`,
Wavelength, ` lamda_1 = 5000 Å`
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_1N_1 =(N_1 hc)/lamda_1`
For a source , `S_2`
wavelength , `lamda_2 = 5100Å`
Number of photons emitted per second , `N_(2) = 1.02 xx 10^(15)`
Energy of each photon , `E_2 = (hc)/(lamda_2)`
Power of source `S_2,P_2=N_2E_2=(N_2hc)/(lamda_2)`
`:. ("Power of "S_2)/("Power of "S_1)=P_2/P_1 =((N_2hc)/(lamda_2))/((N_1hc)/(lamda_1))=(N_2lamda_1)/(N_1lamda_2)`
`=((1.02xx10^(15)" photons/s")xx(5000Å))/((10^(15) " photons/s")xx(5100Å))=51/51 =1`