The dimensional formula for Planck's constant (h) is

Question

Accepted Answer

To find the dimensional formula of Planck's constant ($h$), we can use the equation $E = h
u$, where $E$ is energy and $
u$ is frequency.

1.  **Rearrange the formula:** $h = \frac{E}{
u}$
2.  **Identify Dimensions:**
    *   **Energy ($E$):** Work done = Force $	imes$ Distance. Dimensions = $[ML^2T^{-2}]$.
    *   **Frequency ($
u$):** Inverse of time period. Dimensions = $[T^{-1}]$.
3.  **Calculate Dimensions of $h$:**
    $$ [h] = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-2 - (-1)}] = [ML^2T^{-1}] $$
    Alternatively, the unit of Planck's constant is Joule-second ($J\cdot s$).
    $$ [J\cdot s] = [ML^2T^{-2}] 	imes [T] = [ML^2T^{-1}] $$
    *Note: Planck's constant has the same dimensions as Angular Momentum.*

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