Question 47 of 62intermediate🔧 ApplyNumerical2 marks

In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of 3.15×103.15 \times 10⁻¹⁸ J from the radiations of 600 nm, calculate the number of photons received by the detector.

Correct Answer

The number of photons received by the detector is approximately 9.5.

Exercise: EXERCISES | Q: 2.48 | (Page 41)
For More Understanding

Explanation

To find the number of photons, we first calculate the energy of a single photon using the formula E=hc/λE = hc/\lambda. Then, we divide the total energy received by the detector by the energy of a single photon.

Solution Steps

  1. Step 1: Calculate the energy of one photon Using the formula E=hcλE = \frac{hc}{\lambda}, where h=6.626×10−34h = 6.626 \times 10^{-34} J s, c=3×108c = 3 \times 10^8 m s−1^{-1}, and λ=600\lambda = 600 nm =600×10−9= 600 \times 10^{-9} m: E=6.626×10−34 J s×3×108 m s−1600×10−9 m=3.313×10−19E = \frac{6.626 \times 10^{-34} \text{ J s} \times 3 \times 10^8 \text{ m s}^{-1}}{600 \times 10^{-9} \text{ m}} = 3.313 \times 10^{-19} J

  2. Step 2: Calculate the number of photons The total energy received is 3.15×10−183.15 \times 10^{-18} J. The number of photons is the total energy divided by the energy of one photon: Number of photons = 3.15×10−18 J3.313×10−19 J=9.5\frac{3.15 \times 10^{-18} \text{ J}}{3.313 \times 10^{-19} \text{ J}} = 9.5

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