What is the energy in joule of photon of light whose wave length is 3.0 x` 10^3 `nm

Options

A. 7.5 x `10^(-19)`
B. 6.6 x `10^(-20)`
C. 5.5 x `10^(-20)`
D. 7.5 x `10^(-20)`

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 (\( 3.0 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength (in meters).

### Step-by-Step Solution:

1. **Convert Wavelength from Nanometers to Meters**:
The given wavelength is \( 3.0 \times 10^3 \, \text{nm} \).
To convert nanometers to meters, use the conversion factor \( 1 \, \text{nm} = 10^{-9} \, \text{m} \):
\[ \lambda = 3.0 \times 10^3 \, \text{nm} \times 10^{-9} \, \text{m/nm} = 3.0 \times 10^{-6} \, \text{m} \]

2. **Substitute Values into the Energy Formula**:
Now, substitute \( h \), \( c \), and \( \lambda \) into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.0 \times 10^8 \, \text{m/s})}{3.0 \times 10^{-6} \, \text{m}} \]

3. **Calculate the Energy**:
First, calculate the numerator:
\[ (6.626 \times 10^{-34} \, \text{J s})(3.0 \times 10^8 \, \text{m/s}) = 1.9878 \times 10^{-25} \, \text{J m} \]
Now, divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{3.0 \times 10^{-6} \, \text{m}} = 6.626 \times 10^{-20} \, \text{J} \]

4. **Final Result**:
The energy of the photon is:
\[ E \approx 6.626 \times 10^{-20} \, \text{J} \]

### Summary:
The energy of a photon of light with a wavelength of \( 3.0 \times 10^3 \, \text{nm} \) is approximately \( 6.626 \times 10^{-20} \, \text{J} \).