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JEE Main 202226 JulyMorning Shift
Exam
JEE Main
Year
2022
Date
26 July
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2022 · 26 July · Morning Shift · Physics · Dual Nature of Matter

A parallel beam of light of wavelength 900nm and intensity 100 Wm ^...

A parallel beam of light of wavelength 900nm900nm and intensity 100Wm−2100{Wm}^{- 2} is incident on a surface perpendicular to the beam. The number of photons crossing 1cm21{cm}^{2} area perpendicular to the beam in one second is

Options

  1. A3×10163 \times {10}^{16}
  2. B4.5×10164 . 5 \times {10}^{16}
  3. C4.5×10174 . 5 \times {10}^{17}
  4. D4.5×10204 . 5 \times {10}^{20}

Correct answer

B. 4.5×10164 . 5 \times {10}^{16}

Step-by-step solution

Wavelength of incident beam λ=900×10−9m\lambda = 900 \times {10}^{- 9}m

Energy of a single photon E=hcλE = \dfrac{hc}{\lambda}.

Intensity is defined as power per unit area. Therefore,

Intensity of incident beam I=EtAI = \dfrac{E}{tA}

If the number of photons crossing the given area per second is nn, then

n=EnetEsinglepholon=IAλhcn = \dfrac{{E}_{net}}{{E}_{singlepholon}} = \dfrac{IA\lambda}{hc}

⇒n=(100)(1×10−4)(900×10−9)6.62×10−34×3×108=4.5×1016⇒ n = \dfrac{\left(100\right)\left(1 \times {10}^{- 4}\right)\left(900 \times {10}^{- 9}\right)}{6 . 62 \times {10}^{- 34} \times 3 \times {10}^{8}} = 4 . 5 \times {10}^{16}.

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