JEE Main 2023 · 13 April · evening · Single correct · +4 / −1
Given below are two statements:
Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of above statements, choose the correct answer form the options given below
- (a) Both Statement I and Statement II are true
- (b) Statement I is true but statement II is false
- (c) Statement I is false but statement II is true
- (d) Both Statement I and Statement II are false
Answer and solution
Answer (b) Statement I is true but statement II is false
Solution
Physics sir · 3 steps
Photon energy rises with frequency, so UV wins, and Kₘₐₓ grows linearly with ν, it does not fall.
- Statement I. Each photon carries energy E = hν. Of the three, ultraviolet has the highest frequency, so its photons are the most energetic and the most likely to beat the work function. Microwave and infrared photons usually carry far too little energy to free an electron, however intense the beam. Statement I is true.
Kₘₐₓ = hν - φ₀
- Statement II. Einstein's equation is a straight line in ν with slope h. Above threshold, raising ν raises Kₘₐₓ, so the two cannot be inversely proportional. Statement II is false.
- So. Statement I is true and Statement II is false, which is option (b).
The idea to keep. Whether electrons come out depends on the frequency of each photon, not the brightness of the beam. Kₘₐₓ = hν - φ₀ is linear in ν: it increases with frequency, though it is not strictly proportional to it.
Answer from the NTA final answer key. Solution by PrepWiser.