What is the energy in joule of photon of light whose wave length is 1.0 x` 10^3 `nm

Options

A. 3.5 x `10^(-19)`
B. 1.9 x `10^(-19)`
C. 2.5 x `10^(-19)`
D. 1.5 x `10^(-20)`

Answer

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**:
- Given wavelength \( \lambda = 1.0 \times 10^3 \, \text{nm} \).
- Convert nanometers to meters:
\[ \lambda = 1.0 \times 10^3 \, \text{nm} \times \left( \frac{1 \times 10^{-9} \, \text{m}}{1 \, \text{nm}} \right) = 1.0 \times 10^3 \times 10^{-9} \, \text{m} = 1.0 \times 10^{-6} \, \text{m} \]

2. **Substitute Values into the Energy Formula**:
- Use the values of \( h \), \( c \), and \( \lambda \):
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.0 \times 10^{8} \, \text{m/s})}{1.0 \times 10^{-6} \, \text{m}} \]

3. **Calculate the Energy**:
- Perform the multiplication in the numerator:
\[ E = \frac{(6.626 \times 3.0) \times 10^{-34} \times 10^{8}}{1.0 \times 10^{-6}} \]
\[ = \frac{19.878 \times 10^{-34 + 8 + 6}}{1} = 19.878 \times 10^{-20} \, \text{J} \]
- Simplifying gives:
\[ E \approx 1.988 \times 10^{-19} \, \text{J} \]

4. **Final Result**:
- The energy of the photon is approximately:
\[ E \approx 1.9 \times 10^{-19} \, \text{J} \]

### Conclusion:
The energy of the photon of light with a wavelength of \( 1.0 \times 10^3 \, \text{nm} \) is approximately \( 1.9 \times 10^{-19} \, \text{J} \).