There are `n_(1)` photons of frequency `gamma_(1)` in a beam of light . In an equally energentic beam , there are `n_(2)` photons of frequency `gamma_(2)`. Then the correct relation is

Explanation

To solve the problem, we need to establish the relationship between the number of photons in two beams of light with different frequencies but equal energies. Let's go through the solution step by step.

### Step-by-Step Solution:

1. **Understanding Energy of Photons**:
The energy of a single photon is given by the formula:
\[ E = h \cdot \nu \]
where \( E \) is the energy, \( h \) is Planck's constant, and \( \nu \) (gamma) is the frequency of the photon.

2. **Total Energy of the Beams**:
If there are \( n_1 \) photons in the first beam with frequency \( \gamma_1 \), the total energy \( E_1 \) of the first beam is:
\[ E_1 = n_1 \cdot h \cdot \gamma_1 \]
Similarly, for the second beam with \( n_2 \) photons and frequency \( \gamma_2 \), the total energy \( E_2 \) is:
\[ E_2 = n_2 \cdot h \cdot \gamma_2 \]

3. **Equating the Energies**:
According to the problem, the energies of the two beams are equal:
\[ E_1 = E_2 \]
Substituting the expressions for \( E_1 \) and \( E_2 \):
\[ n_1 \cdot h \cdot \gamma_1 = n_2 \cdot h \cdot \gamma_2 \]

4. **Cancelling Planck's Constant**:
Since \( h \) is a constant and appears on both sides of the equation, we can cancel it out:
\[ n_1 \cdot \gamma_1 = n_2 \cdot \gamma_2 \]

5. **Rearranging the Equation**:
We can rearrange this equation to find the relationship between \( n_1 \) and \( n_2 \):
\[ \frac{n_1}{n_2} = \frac{\gamma_2}{\gamma_1} \]

### Final Relation:
Thus, the correct relation between the number of photons in the two beams is:
\[ n_1 \cdot \gamma_1 = n_2 \cdot \gamma_2 \quad \text{or} \quad \frac{n_1}{n_2} = \frac{\gamma_2}{\gamma_1} \]