Match the LIST-I with LIST-II List-I List-II A. Planck's constant...

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

$[h] = \dfrac{[E]}{[\nu]} = \dfrac{ML^2T^{-2}}{T^{-1}} = ML^2T^{-1}$

The dimensional formula for stopping potential $V_0$ is obtained from $eV_0 = E$.

$[V_0] = \dfrac{[E]}{[e]} = \dfrac{ML^2T^{-2}}{AT} = ML^2T^{-3}A^{-1}$

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

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

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