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Dual Nature of Radiation question

2019 · 10 Apr · Shift 2 · Q68
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Dual Nature of Radiation question

2019 · 10 Apr · Shift 2 · Q68

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108 m/s]
  1. A
    5 × 1015
  2. B
    1.5 × 1016
  3. C
    1 × 1016
  4. D
    2 × 1016
View written solutionFree

Correct answer: A

  1. Given data
  • Power of laser: P=2 mW=2×10−3 WP = 2\,\text{mW} = 2 \times 10^{-3}\,\text{W}P=2mW=2×10−3W
  • Wavelength: λ=500 nm=500×10−9 m=5×10−7 m\lambda = 500\,\text{nm} = 500 \times 10^{-9}\,\text{m} = 5 \times 10^{-7}\,\text{m}λ=500nm=500×10−9m=5×10−7m
  • Planck's constant: h=6.6×10−34 J sh = 6.6 \times 10^{-34}\,\text{J s}h=6.6×10−34J s
  • Speed of light: c=3.0×108 m/sc = 3.0 \times 10^8\,\text{m/s}c=3.0×108m/s
  1. Energy of one photon

The energy of a photon is E=hcλE = \frac{hc}{\lambda}E=λhc​

Substitute the values: E=(6.6×10−34)(3.0×108)5×10−7E = \frac{(6.6 \times 10^{-34})(3.0 \times 10^8)}{5 \times 10^{-7}}E=5×10−7(6.6×10−34)(3.0×108)​

First calculate the numerator: 6.6×3.0=19.86.6 \times 3.0 = 19.86.6×3.0=19.8 10−34×108=10−2610^{-34} \times 10^8 = 10^{-26}10−34×108=10−26 So, hc=19.8×10−26hc = 19.8 \times 10^{-26}hc=19.8×10−26

Now divide by 5×10−75 \times 10^{-7}5×10−7: E=19.8×10−265×10−7E = \frac{19.8 \times 10^{-26}}{5 \times 10^{-7}}E=5×10−719.8×10−26​ E=3.96×10−19 JE = 3.96 \times 10^{-19}\,\text{J}E=3.96×10−19J

  1. Number of photons emitted per second

Power is energy emitted per second, so P=nEP = nEP=nE where nnn is the number of photons emitted per second.

Thus, n=PEn = \frac{P}{E}n=EP​

Substitute values: n=2×10−33.96×10−19n = \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}}n=3.96×10−192×10−3​

n=23.96×1016n = \frac{2}{3.96} \times 10^{16}n=3.962​×1016

n≈0.505×1016=5.05×1015n \approx 0.505 \times 10^{16} = 5.05 \times 10^{15}n≈0.505×1016=5.05×1015

  1. Final answer

The number of photons emitted per second is approximately 5×10155 \times 10^{15}5×1015

So the correct option is A.

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