Study Guides/Physics/Planck's Constant Dimensional Formula
Study Guide · Physics

Planck's Constant — Value and Dimensional Formula

Planck's constant (denoted by h) is a fundamental physical constant in quantum mechanics. Deriving its dimensional formula is a frequent question in Class 11 Physics.

Question (Click to Flip)

Is Planck's constant a dimensionless quantity?

Answer

No, Planck's constant has dimensions [M L² T⁻¹] and units (Joule-second). Dimensionless constants include pure numbers like π or refractive index.

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Key Facts

Max Planck introduced this constant in 1900 to describe the quantization of energy, laying the foundation for all of quantum physics.

Formula and Definition

Planck's constant relates the energy of a photon to its frequency, according to the equation:

E = hν (Where E = Energy, h = Planck's constant, ν = frequency)

Therefore: h = E / ν

Step-by-Step Derivation

  1. Dimension of Energy (E): Energy = Work = Force × Distance E = [M L T⁻²] × [L] = [M L² T⁻²]

  2. Dimension of Frequency (ν): Frequency = 1 / Time period ν = [T⁻¹]

  3. Dimension of Planck's Constant (h): h = [E] / [ν] h = [M L² T⁻²] / [T⁻¹] h = [M L² T⁻²⁺¹] h = [M¹ L² T⁻¹]

Value and Unit

  • SI Unit: Joule-second (J·s)
  • Value: 6.626 × 10⁻³⁴ J·s

Note: The dimensional formula of Planck's constant [M L² T⁻¹] is exactly the same as that of Angular Momentum.

Questions and Answers

Is Planck's constant a dimensionless quantity?+

No, Planck's constant has dimensions [M L² T⁻¹] and units (Joule-second). Dimensionless constants include pure numbers like π or refractive index.

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