JEE Main 2026 — Dual Nature of Matter Question with Solution

The dimensional formula for Planck's constant $h$ is obtained from $E=h\nu$.

$[h]=\frac{[E]}{[\nu ]}=\frac{M{L}^2{T}^{-2}}{T^{-1}}=M{L}^2{T}^{-1}$

The dimensional formula for stopping potential $V_0$ is obtained from $e{V}_0=E$.

$[V_0]=\frac{[E]}{[e]}=\frac{M{L}^2{T}^{-2}}{AT}=M{L}^2{T}^{-3}{A}^{-1}$

Work function is a form of energy, so its dimensional formula is the same as that of energy.

$[\text{Work function}]=M{L}^2{T}^{-2}$

Threshold frequency has the dimensional formula of frequency.

$[\text{Threshold frequency}]=T^{-1}$

Therefore, the correct matching is A-III, B-IV, C-I, D-II.

Answer: A-III, B-IV, C-I, D-II