1.
Photons absorbed in the matter are converted to heat. A source emitting n photons/sec of frequency ν is used to convert 1 kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion:
A
Increases with increasing n, with ν fixed
B
Increases with n fixed, ν increasing
C
Remains constant with n and ν changing such that nν = constant
D
Increases when the product nν increases
View Answer
Correct Answer: C — Remains constant with n and ν changing such that nν = constant
Explanation:
The correct answer is C.
Concept: The energy released or absorbed during a phase change is given by E = mL, where m is the mass of the substance and L is the latent heat.
Derivation:
- Energy required to convert ice to water: mL = 1000 g × 80 cal/g = 80,000 cal
- Total energy delivered by the photon source in time T: E = nT × hν
- Setting them equal: nThν = mL
- Therefore: T = mL / (nhν)
From this expression:
- T ∝ 1/n when ν is constant — so T decreases as n increases (Option 1 is incorrect).
- T ∝ 1/ν when n is constant — so T decreases as ν increases (Option 2 is incorrect).
- If nν = constant, then T = mL / (h × nν) = constant — T remains unchanged (Option 3 is correct).
- If nν increases, T decreases, not increases (Option 4 is incorrect).