What is the energy in joule of photon of light whose wave length is 4.0 x` 10^3 `nm

Options

A. 7.5 x `10^(-19)`
B. 5 x `10^(-20)`
C. 2 x `10^(-10)`
D. 3.5 x `10^(-19)`

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,
- \( h \) 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 \( 4.0 \times 10^{3} \, \text{nm} \). To convert this to meters:
\[ \lambda = 4.0 \times 10^{3} \, \text{nm} \times 10^{-9} \, \text{m/nm} = 4.0 \times 10^{-6} \, \text{m} \]

2. **Substitute Values into the Energy Formula:**
Now that we have \( \lambda \) in meters, we can substitute the values into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.0 \times 10^{8} \, \text{m/s})}{4.0 \times 10^{-6} \, \text{m}} \]

3. **Calculate the Energy:**
Performing the calculation:
\[ E = \frac{(6.626 \times 10^{-34}) \times (3.0 \times 10^{8})}{4.0 \times 10^{-6}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{4.0 \times 10^{-6}} = 4.9695 \times 10^{-20} \, \text{J} \]

4. **Round the Result:**
Rounding \( 4.9695 \times 10^{-20} \, \text{J} \) gives approximately:
\[ E \approx 5.0 \times 10^{-20} \, \text{J} \]

### Final Answer:
The energy of the photon is approximately \( 5.0 \times 10^{-20} \, \text{J} \).

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