The relation between the `"energy" E` and the frequency ` v ` of a photon is repressed by the equation` E = hv `, where h is plank's constant Write down its dimensions.

Explanation

To find the dimensions of Planck's constant \( h \) from the equation \( E = h \nu \), we can follow these steps:

### Step 1: Understand the equation
The equation \( E = h \nu \) relates energy \( E \) to frequency \( \nu \) through Planck's constant \( h \). For the equation to be dimensionally consistent, the dimensions of both sides must be the same.

### Step 2: Rearrange the equation
We can rearrange the equation to express Planck's constant:
\[ h = \frac{E}{\nu} \]

### Step 3: Determine the dimensions of energy \( E \)
Energy can be expressed in terms of force and displacement. The formula for work (or energy) is:
\[ E = \text{Force} \times \text{Displacement} \]
The dimension of force is given by:
\[ \text{Force} = \text{mass} \times \text{acceleration} = \text{kg} \cdot \text{m/s}^2 \]
In dimensional terms, this is:
\[ \text{Force} = [M][L][T^{-2}] \]
Thus, the dimensions of energy \( E \) are:
\[ E = \text{Force} \times \text{Displacement} = [M][L][T^{-2}] \times [L] = [M][L^2][T^{-2}] \]

### Step 4: Determine the dimensions of frequency \( \nu \)
Frequency is defined as the number of cycles per unit time. Therefore, its dimension is:
\[ \nu = \frac{1}{\text{Time}} = [T^{-1}] \]

### Step 5: Substitute the dimensions into the equation for \( h \)
Now we can substitute the dimensions of \( E \) and \( \nu \) into the equation for \( h \):
\[ h = \frac{E}{\nu} = \frac{[M][L^2][T^{-2}]}{[T^{-1}]} = [M][L^2][T^{-2}] \cdot [T] = [M][L^2][T^{-1}] \]

### Step 6: Write down the dimensions of Planck's constant
Thus, the dimensions of Planck's constant \( h \) are:
\[ [h] = [M][L^2][T^{-1}] \]

### Final Answer
The dimensions of Planck's constant \( h \) are \( [M][L^2][T^{-1}] \).

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