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Dual Nature of Radiation question

2021 · 24 Feb · Shift 1 · Q71
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  5. /2021 · 24 Feb · Shift 1 · Q71

Dual Nature of Radiation question

2021 · 24 Feb · Shift 1 · Q71

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
Given below are two statements : Statement I : Two photons having equal linear momenta have equal wavelengths. Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.
  1. A
    Statement I is false but Statement II is true
  2. B
    Both Statement I and Statement II are false
  3. C
    Both Statement I and Statement II are true
  4. D
    Statement I is true but Statement II is false
View written solutionFree

Correct answer: D

  1. Use photon relations

For a photon, p=hλp = \frac{h}{\lambda}p=λh​ and E=hν=hcλE = h\nu = \frac{hc}{\lambda}E=hν=λhc​ where:

  • ppp = momentum
  • EEE = energy
  • λ\lambdaλ = wavelength
  • hhh = Planck's constant
  • ccc = speed of light
  1. Check Statement I

Statement I: Two photons having equal linear momenta have equal wavelengths.

From p=hλp = \frac{h}{\lambda}p=λh​ we get λ=hp\lambda = \frac{h}{p}λ=ph​ So if two photons have equal momentum, then their wavelengths must also be equal.

Hence, Statement I is true.

  1. Check Statement II

Statement II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.

But from the formulas, p=hλ,E=hcλp = \frac{h}{\lambda}, \qquad E = \frac{hc}{\lambda}p=λh​,E=λhc​ If λ\lambdaλ decreases, then both ppp and EEE increase, not decrease.

Hence, Statement II is false.

  1. Choose the correct option
  • Statement I: True
  • Statement II: False

Therefore, the correct option is: D\boxed{\text{D}}D​

  1. Comparison with stored answer

Stored correct answer: D

My derived answer: D

So, the derived answer agrees with the stored correct answer.

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