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Question:

In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of 3.15 × 10⁻¹⁹ J from the radiations of 600 nm, calculate the number of photons received by the detector.

Solution:

The energy of 1 photon, E = hν = hc/λ = (6.626 × 10⁻³⁴ J s × 3.0 × 10⁸ m/s) / (600 × 10⁻⁹ m) = 3.31 × 10⁻¹⁹ J.
The number of photons is (3.15 × 10⁻¹⁹ J) / (3.31 × 10⁻¹⁹ J) = 9.52 ≈ 10.