In astronomical observation, signals observed from the distant st… - Vidyadip

Question

In astronomical observation, 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 600 nm , calculate the number of photons received by the detector.

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Answer

Wavelength $\lambda=600 nm=600 \times 10^{-9} m$, Energy of photon $=3.15 \times 10^{-18} J$
Energy of 1 photon, $E =h v=\frac{h c}{\lambda}$
Energy of $n$ photon $E =\frac{n h c}{\lambda}$
No. of photon, $n=\frac{E \lambda}{h c}$
$=\frac{3.15 \times 10^{-18} J \times 600 \times 10^{-9} m}{6.626 \times 10^{-34} Js \times 3 \times 10^8 ms^{-1}}$
Hence, No. of photons $=9.5=10$

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