What is the energy in joule of photon of light whose wave length is 3 x` 10^5 `nm

Options

A. 6.6 x `10^(-20)`
B. 1.5 x `10^(-19)`
C. 4.5 x `10^(-20)`
D. 6.6 x `10^(-22)`

Explanation

To find the energy of a photon of light with a given wavelength, we can use the formula:

\[ E = \frac{hc}{\lambda} \]

where:
- \( E \) is the energy of the photon in joules,
- \( h \) 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.

### Step-by-Step Solution:

1. **Convert Wavelength from Nanometers to Meters**:
The given wavelength is \( 3 \times 10^{5} \, \text{nm} \). To convert nanometers to meters, we use the conversion factor \( 1 \, \text{nm} = 10^{-9} \, \text{m} \):
\[ \lambda = 3 \times 10^{5} \, \text{nm} \times 10^{-9} \, \text{m/nm} = 3 \times 10^{-4} \, \text{m} \]

2. **Substitute Values into the Energy Formula**:
Now we will substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{3 \times 10^{-4} \, \text{m}} \]

3. **Calculate the Energy**:
First, calculate the numerator:
\[ (6.626 \times 10^{-34} \times 3 \times 10^{8}) = 1.9878 \times 10^{-25} \, \text{J m} \]
Now divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{3 \times 10^{-4} \, \text{m}} = 6.626 \times 10^{-22} \, \text{J} \]

4. **Final Result**:
The energy of the photon is approximately:
\[ E \approx 6.626 \times 10^{-22} \, \text{J} \]

### Conclusion:
The energy of the photon of light with a wavelength of \( 3 \times 10^{5} \, \text{nm} \) is approximately \( 6.626 \times 10^{-22} \, \text{J} \).