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

Options

A. `2.21 xx 10^-35 kg`
B. `2.21 xx 10^-33 g`
C. `2.21 xx 10^-33 kg`
D. `2.21 xx 10^-26 kg`

Explanation

To find the mass of a photon with a wavelength of 1 nm, we can use the relationship between energy, wavelength, and mass. Here's a step-by-step solution:

### Step 1: Understand the relationship
The energy of a photon can be expressed using the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the photon.

### Step 2: Convert wavelength to meters
Given the wavelength \( \lambda = 1 \, \text{nm} \):
\[ \lambda = 1 \, \text{nm} = 1 \times 10^{-9} \, \text{m} \]

### Step 3: Calculate the energy of the photon
Substituting the values into the energy equation:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{1 \times 10^{-9} \, \text{m}} \]

Calculating the numerator:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{Js}}{1 \times 10^{-9} \, \text{m}} \]
\[ E = 1.9878 \times 10^{-16} \, \text{J} \]

### Step 4: Relate energy to mass
Using Einstein's mass-energy equivalence:
\[ E = mc^2 \]
We can rearrange this to find the mass \( m \):
\[ m = \frac{E}{c^2} \]

### Step 5: Substitute the energy and speed of light
Substituting the values we found:
\[ m = \frac{1.9878 \times 10^{-16} \, \text{J}}{(3 \times 10^8 \, \text{m/s})^2} \]
\[ m = \frac{1.9878 \times 10^{-16} \, \text{J}}{9 \times 10^{16} \, \text{m}^2/\text{s}^2} \]

### Step 6: Calculate the mass
\[ m = 2.2098 \times 10^{-33} \, \text{kg} \]

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