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Dual Nature of Radiation question

2007 · Shift 0 · Q67
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Dual Nature of Radiation question

2007 · Shift 0 · Q67

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
Photon of frequency vvv has a momentum associated with it. If ccc is the velocity of light, the momentum is
  1. A
    hv/chv/chv/c
  2. B
    v/cv/cv/c
  3. C
    hvchvchvc
  4. D
    hv/c2hv/{c^2}hv/c2
View written solutionFree

Correct answer: A

  1. For a photon, the energy is given by E=hνE = h\nuE=hν where hhh is Planck's constant and ν\nuν is the frequency.

  2. For electromagnetic radiation (photon), energy and momentum are related by E=pcE = pcE=pc where ppp is the momentum and ccc is the speed of light.

  3. Substitute E=hνE = h\nuE=hν into E=pcE = pcE=pc: hν=pch\nu = pchν=pc

  4. Therefore, p=hνcp = \frac{h\nu}{c}p=chν​

  5. Now compare with the given options:

  • A: hνc\dfrac{h\nu}{c}chν​ ✅
  • B: νc\dfrac{\nu}{c}cν​ ❌
  • C: hνch\nu chνc ❌
  • D: hνc2\dfrac{h\nu}{c^2}c2hν​ ❌

Hence, the correct option is A.

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