Understanding Planck's Constant
Planck's constant is a fundamental quantity in quantum mechanics that relates the energy of a photon to its frequency. It is denoted as "h" and has significant implications in various physical phenomena.
Dimensions of Planck's Constant
The dimensions of Planck's constant can be derived from its definition.
- Energy-Frequency Relation: The energy (E) of a photon is given by the equation E = hν, where ν (nu) is the frequency of the photon.
- Unit of Energy: Energy is measured in joules (J), which can be expressed as kg·m²/s².
- Unit of Frequency: Frequency is measured in hertz (Hz), equivalent to 1/s.
When we analyze the unit of Planck's constant:
- The equation rearranges to h = E/ν.
- This gives us the dimensions of Planck's constant as energy divided by frequency.
Dimensional Analysis
- Using Units:
- Energy (E) = joules (J) = kg·m²/s²
- Frequency (ν) = 1/s
Thus, the dimensions of Planck's constant h can be expressed as:
- h = (kg·m²/s²) / (1/s) = kg·m²/s
Conclusion
Planck's constant does not directly fit into the dimensions of energy, linear momentum, work, or angular momentum. However, it is most closely related to angular momentum because angular momentum has dimensions of mass times velocity times distance (kg·m²/s), which matches the dimensional analysis we conducted for Planck's constant.
In summary, Planck's constant has the dimension of angular momentum.

Angular momentum, I.e. [M1L2T-1]