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).