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Dual Nature of Radiation question

2017 · 9 Apr · Shift 1 · Q54
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Dual Nature of Radiation question

2017 · 9 Apr · Shift 1 · Q54

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are : [Take Planck's constant h === 6.62 ×\times× 10 −-− 34 Js]
  1. A
    1020
  2. B
    1018
  3. C
    1022
  4. D
    1019
View written solutionFree

Correct answer: A

  1. Given data
  • Wavelength of laser: λ=660 nm=660×10−9 m\lambda = 660\,\text{nm} = 660 \times 10^{-9}\,\text{m}λ=660nm=660×10−9m
  • Pulse width: t=60 ms=60×10−3 st = 60\,\text{ms} = 60 \times 10^{-3}\,\text{s}t=60ms=60×10−3s
  • Power: P=0.5 kW=500 WP = 0.5\,\text{kW} = 500\,\text{W}P=0.5kW=500W
  • Planck's constant: h=6.62×10−34 J sh = 6.62 \times 10^{-34}\,\text{J s}h=6.62×10−34J s
  • Speed of light: c≈3×108 m/sc \approx 3 \times 10^8\,\text{m/s}c≈3×108m/s
  1. Energy of the laser pulse

The total energy delivered in one pulse is

Epulse=PtE_{\text{pulse}} = PtEpulse​=Pt

Epulse=500×60×10−3=30 JE_{\text{pulse}} = 500 \times 60 \times 10^{-3} = 30\,\text{J}Epulse​=500×60×10−3=30J

  1. Energy of one photon

Using

Eγ=hcλE_{\gamma} = \frac{hc}{\lambda}Eγ​=λhc​

Eγ=(6.62×10−34)(3×108)660×10−9E_{\gamma} = \frac{(6.62 \times 10^{-34})(3 \times 10^8)}{660 \times 10^{-9}}Eγ​=660×10−9(6.62×10−34)(3×108)​

Eγ=19.86×10−26660×10−9E_{\gamma} = \frac{19.86 \times 10^{-26}}{660 \times 10^{-9}}Eγ​=660×10−919.86×10−26​

Eγ=19.86660×10−17E_{\gamma} = \frac{19.86}{660} \times 10^{-17}Eγ​=66019.86​×10−17

Eγ≈0.0301×10−17=3.01×10−19 JE_{\gamma} \approx 0.0301 \times 10^{-17} = 3.01 \times 10^{-19}\,\text{J}Eγ​≈0.0301×10−17=3.01×10−19J

  1. Number of photons in the pulse

N=EpulseEγN = \frac{E_{\text{pulse}}}{E_{\gamma}}N=Eγ​Epulse​​

N=303.01×10−19N = \frac{30}{3.01 \times 10^{-19}}N=3.01×10−1930​

N≈9.97×1019≈1020N \approx 9.97 \times 10^{19} \approx 10^{20}N≈9.97×1019≈1020

  1. Matching with options

Thus, the approximate number of photons is

1020\boxed{10^{20}}1020​

So the correct option is A.

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