dimensional analysis (planck constant)

Question

Dimensions of Planck's constant h are?

RankGuru · Accepted Answer

1. **Base Equation**: Start from $E = h 
u$ (Photon energy), where $E$ is energy and $
u$ is frequency.
2. **Isolate h**: $h = E / 
u$.
3. **Dimensional Analysis**:
   - $[E] = [ML^2T^{-2}]$
   - $[
u] = [T^{-1}]$ (reciprocal of time period)
4. **Calculation**:
   - $[h] = \frac{[ML^2T^{-2}]}{[T^{-1}]}$
   - $[h] = [ML^2T^{-2+1}] = [ML^2T^{-1}]$.
5. **Note**: These are the same dimensions as **Angular Momentum** ($L = rmv$ or $[L][M][LT^{-1}] = [ML^2T^{-1}]$).

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dimensional analysis (planck constant)

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