What is the momentum of a photon of frequency v ?

Options

A. `(hv)/(c^(2))`
B. `(hv)/(c)`
C. `(v)/(hc)`
D. h v c

Answer

To find the momentum of a photon with frequency \( \nu \), 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 \( h \) is Planck's constant and \( \nu \) is the frequency of the photon.

### Step 2: Relate energy to momentum
We also know that the energy of a photon can be expressed in terms of its momentum \( p \):
\[ E = pc \]
where \( c \) is the speed of light.

### Step 3: Set the two energy expressions equal
Since both expressions represent the energy of the photon, we can set them equal to each other:
\[ h \nu = pc \]

### Step 4: Solve for momentum
Now, we can solve for the momentum \( p \):
\[ p = \frac{h \nu}{c} \]

### Final Result
Thus, the momentum of a photon of frequency \( \nu \) is:
\[ p = \frac{h \nu}{c} \]