Question 45 of 62intermediate🔧 ApplyNumerical3 marks

Nitrogen laser produces a radiation at a wavelength of 337.1 nm. If the number of photons emitted is 5.6×105.6 \times 10²⁴, calculate the power of this laser.

Correct Answer

3.30×1063.30 \times 10^6 W (assuming the photons are emitted in 1 second)

Exercise: EXERCISES | Q: 2.46 | (Page 41)
For More Understanding

Explanation

To find the power of the laser, we first calculate the energy of a single photon using Planck's equation E=hc/λE = hc/\lambda. Then, we multiply this energy by the total number of photons to get the total energy emitted. Since the time duration of emission is not provided in the question, it is standard to assume a time of 1 second to calculate the power in Watts (Joules per second).

Solution Steps

  1. Step 1: Calculate the energy of one photon using the formula E=hcλE = \frac{hc}{\lambda}. Given h=6.626×10−34h = 6.626 \times 10^{-34} J s, c=3×108c = 3 \times 10^8 m/s, and λ=337.1×10−9\lambda = 337.1 \times 10^{-9} m. E=6.626×10−34×3×108337.1×10−9=5.89×10−19E = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{337.1 \times 10^{-9}} = 5.89 \times 10^{-19} J.

  2. Step 2: Calculate the total energy emitted by all photons. Given the number of photons N=5.6×1024N = 5.6 \times 10^{24}. Total Energy =N×E=5.6×1024×5.89×10−19=3.30×106= N \times E = 5.6 \times 10^{24} \times 5.89 \times 10^{-19} = 3.30 \times 10^6 J.

  3. Step 3: Calculate the power of the laser. Power is energy per unit time. Assuming the total energy is emitted in t=1t = 1 second, Power =Total Energytime=3.30×106 J1 s=3.30×106= \frac{\text{Total Energy}}{\text{time}} = \frac{3.30 \times 10^6 \text{ J}}{1 \text{ s}} = 3.30 \times 10^6 W.

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