Dynamic mass of the photon in usual notations is given by

Options

A. `(hv)/(c)`
B. `(h lambda)/(c)`
C. `(h)/( c lambda)`
D. `(h)/(cv)`

Answer

To find the dynamic mass of a photon, we can start from the relationship between energy, momentum, and mass in the context of relativity and quantum mechanics. Here’s a step-by-step solution:

### Step 1: Understand the relationship between energy and momentum of a photon
The energy (E) of a photon is given by the equation:
\[ E = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the photon.

### Step 2: Relate frequency to wavelength
The frequency \( \nu \) can be related to the wavelength \( \lambda \) of the photon using the equation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light.

### Step 3: Substitute frequency in the energy equation
Substituting the expression for frequency into the energy equation gives:
\[ E = h \frac{c}{\lambda} \]

### Step 4: Use the relationship between energy and momentum
The momentum \( p \) of a photon is given by:
\[ p = \frac{E}{c} \]
Substituting the expression for energy from Step 3, we have:
\[ p = \frac{h c}{\lambda c} = \frac{h}{\lambda} \]

### Step 5: Relate momentum to mass
In relativistic physics, the momentum of a particle is also related to its mass (m) and velocity (v) by the equation:
\[ p = mv \]
For a photon, which travels at the speed of light, we can express the mass in terms of momentum:
\[ m = \frac{p}{c} \]

### Step 6: Substitute the expression for momentum
Substituting the expression for momentum from Step 4 into the mass equation gives:
\[ m = \frac{h/\lambda}{c} \]

### Final Expression
Thus, the dynamic mass of the photon can be expressed as:
\[ m = \frac{h}{\lambda c} \]