The mass of photon having wavelength `1 nm` is :

Answer

To find the mass of a photon with a wavelength of 1 nm, we can use the relationship between the energy of a photon and its wavelength. The mass of a photon can be derived from its energy using Einstein's mass-energy equivalence principle.

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
- The given wavelength is 1 nm (nanometer).
- Convert nanometers to meters:
\[ 1 \text{ nm} = 1 \times 10^{-9} \text{ m} \]

2. **Use the Energy-Wavelength Relationship**:
- The energy \( E \) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
- Where:
- \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \)
- \( c \) is the speed of light \( (3 \times 10^{8} \text{ m/s}) \)
- \( \lambda \) is the wavelength in meters \( (1 \times 10^{-9} \text{ m}) \)

3. **Substitute Values into the Energy Formula**:
- Plugging in the values:
\[ E = \frac{(6.626 \times 10^{-34} \text{ J s})(3 \times 10^{8} \text{ m/s})}{1 \times 10^{-9} \text{ m}} \]

4. **Calculate the Energy**:
- Performing the calculation:
\[ E = \frac{(6.626 \times 10^{-34})(3 \times 10^{8})}{1 \times 10^{-9}} = 1.9878 \times 10^{-14} \text{ J} \]

5. **Use Einstein's Mass-Energy Equivalence**:
- According to Einstein's equation, \( E = mc^2 \), we can find the mass \( m \):
\[ m = \frac{E}{c^2} \]
- Substituting the value of \( E \):
\[ m = \frac{1.9878 \times 10^{-14} \text{ J}}{(3 \times 10^{8} \text{ m/s})^2} \]

6. **Calculate the Mass**:
- Performing the calculation:
\[ m = \frac{1.9878 \times 10^{-14}}{9 \times 10^{16}} = 2.21 \times 10^{-33} \text{ kg} \]

7. **Final Answer**:
- The mass of the photon having a wavelength of 1 nm is:
\[ m \approx 2.21 \times 10^{-33} \text{ kg} \]