Planck's constant has dimensions …………….

Explanation

To determine the dimensions of Planck's constant, we can use the relationship between energy and frequency. The formula we will use is:

\[ E = h \nu \]

Where:
- \( E \) is energy,
- \( h \) is Planck's constant,
- \( \nu \) (nu) is frequency.

### Step 1: Rearranging the formula
From the equation \( E = h \nu \), we can express Planck's constant \( h \) as:

\[ h = \frac{E}{\nu} \]

### Step 2: Identifying the dimensions of energy
The dimensions of energy \( E \) can be expressed as:

\[ [E] = [M][L^2][T^{-2}] \]

Where:
- \( [M] \) is mass,
- \( [L] \) is length,
- \( [T] \) is time.

### Step 3: Identifying the dimensions of frequency
The dimensions of frequency \( \nu \) are:

\[ [\nu] = [T^{-1}] \]

### Step 4: Substituting the dimensions into the formula
Now, substituting the dimensions of energy and frequency into the equation for \( h \):

\[ [h] = \frac{[E]}{[\nu]} = \frac{[M][L^2][T^{-2}]}{[T^{-1}]} \]

### Step 5: Simplifying the dimensions
When we simplify the expression:

\[ [h] = [M][L^2][T^{-2}] \cdot [T] = [M][L^2][T^{-1}] \]

### Final Answer
Thus, the dimensions of Planck's constant \( h \) are:

\[ [h] = [M][L^2][T^{-1}] \]

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