Planck's constant has dimension ………………………….. .

Explanation

To find the dimension of Planck's constant (H), we start with the relationship between energy (E) and frequency (ν):

1. **Understanding the Relationship**:
The equation relating energy and frequency is given by:
\[ E = H \nu \]
where \(E\) is energy, \(H\) is Planck's constant, and \(\nu\) is frequency.

2. **Identifying Dimensions**:
We know the dimensions of energy and frequency:
- The dimension of energy (E) can be expressed as:
\[ [E] = [\text{Force}] \times [\text{Distance}] = [M L T^{-2}] \times [L] = [M L^2 T^{-2}] \]
- The dimension of frequency (\(\nu\)) is the reciprocal of time:
\[ [\nu] = [T^{-1}] \]

3. **Rearranging the Equation**:
From the equation \(E = H \nu\), we can rearrange it to find the dimension of Planck's constant:
\[ H = \frac{E}{\nu} \]

4. **Substituting Dimensions**:
Now substituting the dimensions we found:
\[ [H] = \frac{[E]}{[\nu]} = \frac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-2}] \times [T] = [M L^2 T^{-1}] \]

5. **Final Result**:
Therefore, the dimension of Planck's constant (H) is:
\[ [H] = [M^1 L^2 T^{-1}] \]

### Summary:
The dimension of Planck's constant is \(M^1 L^2 T^{-1}\).