Find the effective mass of a photon if the wavelength of radiation is `6xx10^(14)Hz`.

Explanation

To find the effective mass of a photon given the wavelength of radiation, we can follow these steps:

### Step 1: Understand the relationship between wavelength and frequency
The frequency (ν) of the radiation is related to its wavelength (λ) by the equation:
\[ c = \lambda \cdot \nu \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 2: Calculate the frequency from the wavelength
Given the frequency \( \nu = 6 \times 10^{14} \, \text{Hz} \), we can directly use this value in our calculations for energy and mass.

### Step 3: Use the energy-mass relationship for photons
The energy (E) of a photon can be expressed as:
\[ E = h \cdot \nu \]
where \( h \) is Planck's constant, approximately \( 6.63 \times 10^{-34} \, \text{Js} \).

### Step 4: Substitute the values to find energy
Substituting the values into the equation:
\[ E = (6.63 \times 10^{-34} \, \text{Js}) \cdot (6 \times 10^{14} \, \text{Hz}) \]
Calculating this gives:
\[ E = 3.978 \times 10^{-19} \, \text{J} \]

### Step 5: Relate energy to effective mass
Using Einstein's mass-energy equivalence, we can relate the energy to mass:
\[ E = m \cdot c^2 \]
Thus, the effective mass \( m \) of the photon can be calculated as:
\[ m = \frac{E}{c^2} \]

### Step 6: Substitute the values to find effective mass
Substituting the values of \( E \) and \( c \):
\[ m = \frac{3.978 \times 10^{-19} \, \text{J}}{(3 \times 10^8 \, \text{m/s})^2} \]
Calculating \( c^2 \):
\[ c^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]
Now substituting this into the mass equation:
\[ m = \frac{3.978 \times 10^{-19}}{9 \times 10^{16}} \]
Calculating this gives:
\[ m \approx 4.42 \times 10^{-36} \, \text{kg} \]

### Final Answer
The effective mass of the photon is approximately:
\[ m \approx 4.42 \times 10^{-36} \, \text{kg} \]

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