The mass of photon of wavelength `lambda` is given by

Options

A. `hlambdac`
B. `h//lambdac`
C. `hc//lambda`
D. `hlambda//c`

Answer

To find the mass of a photon with a given wavelength \( \lambda \), we can follow these steps:

### Step 1: Understand the relationship between momentum and wavelength
The momentum \( p \) of a photon is given by the equation:
\[ p = \frac{h}{\lambda} \]
where \( h \) is Planck's constant and \( \lambda \) is the wavelength of the photon.

### Step 2: Relate momentum to mass and velocity
For any particle, the momentum can also be expressed as:
\[ p = mv \]
where \( m \) is the mass of the particle and \( v \) is its velocity. For a photon, the velocity \( v \) is the speed of light \( c \).

### Step 3: Substitute the speed of light into the momentum equation
For a photon, we can substitute \( v \) with \( c \):
\[ p = mc \]

### Step 4: Set the two expressions for momentum equal to each other
Since both expressions represent the momentum of the photon, we can set them equal:
\[ \frac{h}{\lambda} = mc \]

### Step 5: Solve for the mass \( m \)
Now, we can rearrange this equation to solve for the mass \( m \):
\[ m = \frac{h}{\lambda c} \]

### Conclusion
Thus, the mass of a photon with wavelength \( \lambda \) is given by:
\[ m = \frac{h}{\lambda c} \]