In astronomical observations, signals observed from the distant s… - Vidyadip

Question

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

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Answer

From the expression of energy of one photon (E),
$\text{E}=\frac{\text{hc}}{\lambda}$
Where,
$\lambda$ = wavelength of radiation
h = Planck’s constant
c = velocity of radiation
Substituting the values in the given expression of E:
$\text{E}=\frac{(6.626\times10^{-34}\text{Js})(3\times10^8\text{ms}^{-1})}{(600\times0^{-9}\text{m})}$
$E = 3.313 \times 10^{–19}J$
Energy of one photon = $3.313 \times 10^{–19}J$
Number of photons received with $3.15 \times 10^{–18}J$ energy
$=\frac{3.15\times10^{-18}\text{J}}{3.313\times10^{-19}\text{J}}$
$=9.5$
$\approx10$

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