Question

Matching type questions: (Match, Column-I and Column-II property) Column-I Column-II (I) Energy of photon of wavelength \(\lambda\) is (P) \((\mathrm{E} / \mathrm{p})\) (II) The de Broglie wavelength associated (Q) \(\left(\mathrm{hf} / \mathrm{c}^{2}\right)\) with particle of momentum \(\mathrm{P}\) is (II) Mass of photon in motion is (R) (hc \(/ \lambda\) ) (IV) The velocity of photon of energy (S) \((\mathrm{h} / \mathrm{p})\) \(\mathrm{E}\) and momentum \(\mathrm{P}\) is (A) I - P, II - Q. III - R, IV - S (B) $\mathrm{I}-\mathrm{R}, \mathrm{II}-\mathrm{S}, \mathrm{III}-\mathrm{Q}, \mathrm{IV}-\mathrm{P}$ (C) $\mathrm{I}-\mathrm{R}, \mathrm{II}-\mathrm{S}, \mathrm{III}-\mathrm{P}_{3} \mathrm{IV}-\mathrm{Q}$ (D) $\mathrm{I}-\mathrm{S}, \mathrm{II}-\mathrm{R}, \mathrm{III}-\mathrm{Q}, \mathrm{IV}-\mathrm{P}$

Short answer

(B) I - R, II - S, III - Q, IV - P

Step-by-step solution

Energy of Photon

The energy of a photon with a wavelength λ is given by the Planck's formula: \(E = h\frac{c}{\lambda}\) Where, \(E\) = energy of the photon, \(h\) = Planck's constant, \(c\) = speed of light, \(\lambda\) = wavelength. We will look to match this formula in Column-II.

de Broglie Wavelength

The de Broglie wavelength associated with a particle of momentum P is given by de Broglie's formula: \(\lambda = \frac{h}{P}\) Where, \(\lambda\) = wavelength, \(h\) = Planck's constant, \(P\) = momentum. We will look to match this formula in Column-II.

Mass of Photon

A photon has no rest mass. But when the photon is in motion, it has mass given by the formula: \(m = \frac{hf}{c^2}\) Where, \(m\) = mass of the photon, \(h\) = Planck's constant, \(f\) = frequency of the photon, \(c\) = speed of light. We will look to match this formula in Column-II.

Velocity of Photon

The velocity of a photon remains constant and is equal to the speed of light (c). There is no need to find a formula in Column-II for this property, as it is a simple constant value.

Matching the Properties

Now, let's match the formulas for each property in Column-I to the corresponding formula in Column-II: (I) Energy of photon of wavelength λ is: (R) \((hc / \lambda)\) (II) The de Broglie wavelength associated with particle of momentum P is: (S) \((h / p)\) (III) Mass of photon in motion is: (Q) \((hf / c^2)\) Thus, the correct match of the given properties is: I - R, II - S, III - Q The correct answer is Option (B): I - R, II - S, III - Q, IV - P.