Question

In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of 3.15 × ${10}^{–18}$ J from the radiations of 600 nm, calculate the number of photons received by the detector.

Answer 1

From the expression of energy of one photon (E),
$E=\frac{hc}{\lambda }$
Where, λ = wavelength of radiation
h = Planck’s constant
c = velocity of radiation
Substituting the values in the given expression of E:
$E=\frac{(6.626\times {10}^{-34}Js)(3\times {10}^{8}m{s}^{-1})}{(600\times {10}^{-9m})}=3.313\times {10}^{-19}J$
Energy of one photon = 3.313 × ${10}^{–19}$ J
Number of photons received with 3.15 × ${10}^{–18}$ J energy
$\frac{3.15\times {10}^{-18}J}{3.313\times {10}^{-19}J}=9.5\approx 10$