Dimensional Analysis Of Constants

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While studying photon energy, a learner encounters Planck's constant in the relation linking energy and frequency of emitted light. What is the dimensional formula of Planck's constant?

RankGuru · Accepted Answer

Drawing on NCERT Class 11, Chapter 2 (Units and Measurements), a constant's dimensions follow from its defining equation. Planck's constant h appears in E = h ν, where E is energy and ν is frequency, so h = E / ν. Energy has dimensions [M^{1}L^{2}T^{-2}] and frequency has dimensions [T^{-1}] since it is the inverse of time. Dividing gives h = [M^{1}L^{2}T^{-2}] / [T^{-1}] = [M^{1}L^{2}T^{-1}]. The option [M^{1}L^{2}T^{-2}] is wrong because it equals energy, the numerator, not the constant. The option [M^{1}L^{1}T^{-1}] is wrong as the length power is incorrect. The option [M^{1}L^{2}T^{-3}] is wrong since it matches power, not Planck's constant. A final check confirms that Planck's constant shares its dimensions with angular momentum, which is consistent with its appearance in quantised angular momentum expressions.

Dimensional Analysis Of Constants

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