For given enegy, corresponding wavelength will be `E = 3.03 xx 10^(-19)` Joules `(h = 6.6 xx 10^(-34) j X` sec., `C = 3 xx 10^(8)` m/sec

Options

A. 65.3 nm.
B. 6.53 nm
C. 3.4 nm
D. 653 nm

Answer

To find the corresponding wavelength for the given energy, we can use the relationship between energy (E) and wavelength (λ), which is given by the formula:

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

Where:
- \( E \) is the energy in joules,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \) J·s),
- \( c \) is the speed of light (\( 3 \times 10^{8} \) m/s),
- \( \lambda \) is the wavelength in meters.

### Step-by-Step Solution:

1. **Rearranging the formula to solve for wavelength (λ)**:
\[ \lambda = \frac{hc}{E} \]

2. **Substituting the known values**:
- \( h = 6.63 \times 10^{-34} \) J·s
- \( c = 3 \times 10^{8} \) m/s
- \( E = 3.03 \times 10^{-19} \) J

Substituting these values into the equation:
\[ \lambda = \frac{(6.63 \times 10^{-34} \, \text{J·s}) \times (3 \times 10^{8} \, \text{m/s})}{3.03 \times 10^{-19} \, \text{J}} \]

3. **Calculating the numerator**:
\[ 6.63 \times 10^{-34} \times 3 \times 10^{8} = 1.989 \times 10^{-25} \, \text{J·m} \]

4. **Calculating the wavelength (λ)**:
\[ \lambda = \frac{1.989 \times 10^{-25}}{3.03 \times 10^{-19}} \approx 6.53 \times 10^{-7} \, \text{m} \]

5. **Converting meters to nanometers**:
Since \( 1 \, \text{m} = 10^{9} \, \text{nm} \):
\[ \lambda = 6.53 \times 10^{-7} \, \text{m} \times 10^{9} \, \text{nm/m} = 653 \, \text{nm} \]

### Final Answer:
The corresponding wavelength for the given energy is **653 nanometers**.