Calculate the effective mass of a photon with frequency of `6.2 xx 10^(14)` Hz.

Answer

To calculate the effective mass of a photon with a frequency of \(6.2 \times 10^{14}\) Hz, we can follow these steps:

### Step 1: Understand the relationship between energy and frequency
The energy \(E\) of a photon is given by the equation:
\[ E = h \nu \]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(\nu\) is the frequency of the photon.

### Step 2: Calculate the energy of the photon
Substituting the values into the equation:
\[ E = (6.626 \times 10^{-34} \, \text{J s}) \times (6.2 \times 10^{14} \, \text{Hz}) \]
Calculating this gives:
\[ E = 4.112 \times 10^{-19} \, \text{J} \]

### Step 3: Use Einstein's mass-energy equivalence
According to Einstein's mass-energy equivalence principle, the effective mass \(m\) of the photon can be calculated using the equation:
\[ E = mc^2 \]
Rearranging this gives:
\[ m = \frac{E}{c^2} \]
where \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).

### Step 4: Substitute the values to find the effective mass
Substituting the energy and the speed of light into the equation:
\[ m = \frac{4.112 \times 10^{-19} \, \text{J}}{(3 \times 10^8 \, \text{m/s})^2} \]
Calculating \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]
Now substituting this back into the mass equation:
\[ m = \frac{4.112 \times 10^{-19}}{9 \times 10^{16}} \approx 4.57 \times 10^{-36} \, \text{kg} \]

### Final Answer
The effective mass of the photon is approximately:
\[ m \approx 4.57 \times 10^{-36} \, \text{kg} \]