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JEE Main 2022 (26 Jul, Shift 1) · Photons: Energy, Momentum & Radiation Pressure

Photons: Energy, Momentum & Radiation Pressure question from JEE Main 2022 (26 Jul, Shift 1)

Q21JEE Main 2022 · 26 JUL · SHIFT 1Medium

Photons: Energy, Momentum & Radiation Pressure

A parallel beam of light of wavelength 900 nm900\text{ nm} and intensity 100 Wm−2100\text{ Wm}^{-2} is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm21\text{ cm}^{2} area perpendicular to the beam in one second is:

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Answer: (b)

  1. Power through 1 cm21\text{ cm}^2: P=IA=100×10−4=10−2 WP = IA = 100\times10^{-4} = 10^{-2}\text{ W}
  2. Photon energy hcλ=6.63×10−34×3×108900×10−9=2.21×10−19 J\dfrac{hc}{\lambda} = \dfrac{6.63\times10^{-34}\times3\times10^{8}}{900\times10^{-9}} = 2.21\times10^{-19}\text{ J}
  3. n=10−22.21×10−19≈4.5×1016n = \dfrac{10^{-2}}{2.21\times10^{-19}} \approx 4.5\times10^{16} per second
  4. So the answer is (b) 4.5×10164.5\times10^{16}.
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