JEE Main 2021 · 24 February · morning · Single correct · +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.
- (a) Statement I is false but Statement II is true
- (b) Both Statement I and Statement II are false
- (c) Both Statement I and Statement II are true
- (d) Statement I is true but Statement II is false
Answer and solution
Answer (d) Statement I is true but Statement II is false
Solution
Physics sir · 4 steps
For a photon, momentum and wavelength are locked together by p = h/λ: read both statements off that.
- The two relations. A photon's momentum is p = h/λ and its energy is E = hc/λ. Both have λ in the denominator, so both go up when λ goes down.
p = h/λ, E = hc/λ = pc
- Statement I. Rearranging gives λ = h/p, and h is the same constant for every photon. Equal momenta therefore give equal wavelengths, so Statement I is true.
- Statement II. If λ decreases, h/λ and hc/λ both increase. Momentum and energy rise, they do not fall, so Statement II is false.
- So. Statement I is true and Statement II is false, which is option (d).
The idea to keep. For a photon, p = h/λ and E = hc/λ. Shorter wavelength always means more momentum and more energy. Think of X-rays versus radio waves.
Answer from the NTA final answer key. Solution by PrepWiser.