If the total energy of radiation of frequency `10^(14)Hz is 6.63 J , Calculate the number of photons in the radiation

Answer

To solve the problem of calculating the number of photons in the radiation, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Total energy (E) = 6.63 J
- Frequency (ν) = \(10^{14}\) Hz

2. **Calculate the energy of one photon**:
The energy of one photon (E₀) can be calculated using the formula:
\[ E₀ = hν \]
where \(h\) is Planck's constant, approximately \(6.63 \times 10^{-34} \, \text{J s}\).

3. **Substitute the values into the formula**:
\[ E₀ = (6.63 \times 10^{-34} \, \text{J s}) \times (10^{14} \, \text{Hz}) \]

4. **Perform the multiplication**:
\[ E₀ = 6.63 \times 10^{-34} \times 10^{14} = 6.63 \times 10^{-20} \, \text{J} \]

5. **Calculate the number of photons (n)**:
The number of photons can be found by dividing the total energy by the energy of one photon:
\[ n = \frac{E}{E₀} \]
Substituting the known values:
\[ n = \frac{6.63 \, \text{J}}{6.63 \times 10^{-20} \, \text{J}} \]

6. **Simplify the equation**:
\[ n = \frac{6.63}{6.63 \times 10^{-20}} = 10^{20} \]

### Final Answer:
The number of photons in the radiation is \(n = 10^{20}\).