Numford

Fundamental constantsClass 12, Dual Nature of Radiation and Matter

Dimensional formula of Planck's constant

[M L2 T-1]

Symbolh SI unitjoule second (J s)

The constant in E = hν. It has the dimension of angular momentum.

Derivation

How to get the dimensional formula of Planck's constant

  1. Start from the definition: Planck's constant = energy × time.
  2. velocity = length / time, so velocity is [L] / [T] = [L T-1].
  3. energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
  4. Put in the dimension of each part: [M L2 T-2] × [T].
  5. Add the powers of each base quantity: [M L2 T-1].
Same dimensions

Quantities with the dimensions [M L² T⁻¹]

Equal dimensions do not make them the same quantity. Compare Planck's constant with the others in the full grid.

Practice

Three questions on Planck's constant

1Which of these has the same dimensions as Planck's constant?

2What is the SI unit of Planck's constant?

3Which one has different dimensions from the others?

Try it

An equation that uses Planck's constant

Equation checker

Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.

Read asλ = h / (m v)
lambda[L]h/mv[L]
Dimensionally consistentEvery term is [L]
v = velocity
Questions

Planck's constant: quick answers

What is the dimensional formula of Planck's constant?

The dimensional formula of Planck's constant is [M L² T⁻¹]. It comes from Planck's constant = energy × time.

What is the SI unit of Planck's constant?

The SI unit of Planck's constant is the joule second (J s).

Which quantities have the same dimensions as Planck's constant?

Planck's constant shares [M L² T⁻¹] with angular momentum, angular impulse, reduced Planck's constant (h-bar). Equal dimensions do not make them the same quantity.

Open the dimensional formula tool