Dimensional Analysis Of Constants
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?
Select the correct option:
Solution
[M1L2T−1]
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.
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- dimensional analysis of constants
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
[M1L2T−1]
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.
This hard difficulty physics question is from the chapter physics and measurement, covering the topic of dimensional analysis of constants. It appeared in the 2025 exam.
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