Dual Nature of Matter

JEE Main level, single correct, medium

93 of 200

Question 93 of 200

Match the LIST-I with LIST-II
List-IList-IIA. Planck's constantI. ML2T−2ML^2T^{-2}B. Stopping potentialII. T−1T^{-1}C. Work functionIII. ML2T−1ML^2T^{-1}D. Threshold frequencyIV. ML2T−3A−1ML^2T^{-3}A^{-1}
Choose the correct answer from the options given below:

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

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

[h]=[E][ν]=ML2T−2T−1=ML2T−1[h] = \dfrac{[E]}{[\nu]} = \dfrac{ML^2T^{-2}}{T^{-1}} = ML^2T^{-1}

The dimensional formula for stopping potential V0V_0 is obtained from eV0=EeV_0 = E.

[V0]=[E][e]=ML2T−2AT=ML2T−3A−1[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.

[Work function]=ML2T−2[\text{Work function}] = ML^2T^{-2}

Threshold frequency has the dimensional formula of frequency.

[Threshold frequency]=T−1[\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

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