Momentum of a photon of wavelength `lamda` is

Options

A. `(h)/(lamda)`
B. Zero
C. `(h lamda)/(c^(2))`
D. `(h lamda)/(c)`

Answer

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

### Step-by-Step Solution:

1. **Understand the relationship between energy, frequency, and wavelength**:
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.

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

3. **Substitute frequency into the energy equation**:
By substituting the expression for frequency into the energy equation, we have:
\[ E = h \left(\frac{c}{\lambda}\right) = \frac{hc}{\lambda} \]

4. **Use the relationship between energy and momentum**:
The momentum \( P \) of a photon can be expressed in terms of its energy:
\[ P = \frac{E}{c} \]

5. **Substitute the energy expression into the momentum equation**:
Now, substituting the expression for energy into the momentum equation:
\[ P = \frac{hc/\lambda}{c} \]

6. **Simplify the equation**:
The \( c \) in the numerator and denominator cancels out:
\[ P = \frac{h}{\lambda} \]

### Final Result:
Thus, the momentum of a photon of wavelength \( \lambda \) is given by:
\[ P = \frac{h}{\lambda} \]