Match List-I with List-II
| List-I | List-II | ||
| (Physical Quantity) | (Dimensions) | ||
| (A) | Stopping Potential | (I) | [T−1] |
| (B) | Work Function | (II) | [ML2T−1] |
| (C) | Planck's Constant | (III) | [ML2T−3A−1] |
| (D) | Threshold Frequency | (IV) | [ML2T−2] |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
Start from the dimensions of energy, [ML2T−2], and use the defining relations of the photoelectric effect.
(A) Stopping Potential — this matches (III) [ML2T−3A−1]. A potential is energy per unit charge, and charge = current × time.
\( \displaystyle [V] = \frac{[\mathrm{ML^{2}T^{-2}}]}{[\mathrm{AT}]} = [\mathrm{ML^{2}T^{-3}A^{-1}}] \)
(B) Work Function — this matches (IV) [ML2T−2]. The work function is the minimum energy needed to free an electron, so it has the dimensions of energy.
(C) Planck's Constant — this matches (II) [ML2T−1]. From \( E = h\nu \), h is energy divided by frequency.
\( \displaystyle [h] = \frac{[\mathrm{ML^{2}T^{-2}}]}{[\mathrm{T^{-1}}]} = [\mathrm{ML^{2}T^{-1}}] \)
(D) Threshold Frequency — this matches (I) [T−1]. Any frequency has the dimensions of 1/time.