Numford

Fundamental constantsClass 12, Dual Nature of Radiation and Matter

Dimensional formula of Reduced Planck's constant (h-bar)

[M L2 T-1]

Symbolħ SI unitjoule second (J s)

Planck's constant divided by 2π, written ħ. It has the same dimension as h and as angular momentum.

Derivation

How to get the dimensional formula of reduced Planck's constant (h-bar)

  1. Start from the definition: reduced Planck's constant (h-bar) = plancks constant / angle.
  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. Planck's constant = energy × time, so Planck's constant is [M L2 T-2] × [T] = [M L2 T-1].
  5. angle = length / length, so angle is [L] / [L] = [M0 L0 T0].
  6. Put in the dimension of each part: [M L2 T-1] / [M0 L0 T0].
  7. 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 reduced Planck's constant (h-bar) with the others in the full grid.

Practice

Three questions on reduced Planck's constant (h-bar)

1Which of these has the same dimensions as reduced Planck's constant (h-bar)?

2What is the SI unit of reduced Planck's constant (h-bar)?

3Which one has different dimensions from the others?

Questions

Reduced Planck's constant (h-bar): quick answers

What is the dimensional formula of reduced Planck's constant (h-bar)?

The dimensional formula of reduced Planck's constant (h-bar) is [M L² T⁻¹]. It comes from reduced Planck's constant (h-bar) = plancks constant / angle.

What is the SI unit of reduced Planck's constant (h-bar)?

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

Which quantities have the same dimensions as reduced Planck's constant (h-bar)?

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

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