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JEE Main 2023 (31 Jan, Shift 1) · Photons: Energy, Momentum & Radiation Pressure

Photons: Energy, Momentum & Radiation Pressure question from JEE Main 2023 (31 Jan, Shift 1)

Q19JEE Main 2023 · 31 JAN · SHIFT 1Medium

Photons: Energy, Momentum & Radiation Pressure

If a source of electromagnetic radiation having power 15 kW15\text{ kW} produces 101610^{16} photons per second, the radiation belongs to a part of spectrum is.

(Take Planck constant h=6×10−34 Jsh = 6 \times 10^{-34}\text{ Js})

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Answer: (a)

  1. Energy per photon E=Pn=15×1031016=1.5×10−12 JE = \dfrac{P}{n} = \dfrac{15\times10^{3}}{10^{16}} = 1.5\times10^{-12}\text{ J}
  2. λ=hcE=6×10−34×3×1081.5×10−12=1.2×10−13 m\lambda = \dfrac{hc}{E} = \dfrac{6\times10^{-34}\times3\times10^{8}}{1.5\times10^{-12}} = 1.2\times10^{-13}\text{ m}
  3. E≈9 MeVE \approx 9\text{ MeV} and λ∼10−13 m\lambda \sim 10^{-13}\text{ m}: gamma-ray region.
  4. So the answer is (a) Gamma rays.
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