What is the wavelength of light . Given energy `=3.03xx10^(-19)J, h=6.6xx10^(-34)JS, c=3.0xx10^(8)m//s`?

Options

A. 6.54 nm
B. 654 nm
C. 0.654 nm
D. 65.4 nm

Explanation

To find the wavelength of light given its energy, we can use the formula that relates energy (E), Planck's constant (h), the speed of light (c), and wavelength (λ):

### Step-by-Step Solution:

1. **Identify the Formula**:
The energy of a photon can be expressed as:
\[ E = \frac{hc}{\lambda} \]
Rearranging this formula to solve for wavelength (λ) gives:
\[ \lambda = \frac{hc}{E} \]

2. **Substitute the Given Values**:
We have:
- Energy, \( E = 3.03 \times 10^{-19} \, \text{J} \)
- Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- Speed of light, \( c = 3.0 \times 10^{8} \, \text{m/s} \)

Plugging these values into the rearranged formula:
\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3.0 \times 10^{8} \, \text{m/s})}{3.03 \times 10^{-19} \, \text{J}} \]

3. **Calculate the Numerator**:
First, calculate the numerator:
\[ (6.626 \times 10^{-34}) \times (3.0 \times 10^{8}) = 1.9878 \times 10^{-25} \, \text{Js m/s} \]

4. **Calculate the Wavelength**:
Now, divide the result by the energy:
\[ \lambda = \frac{1.9878 \times 10^{-25}}{3.03 \times 10^{-19}} \approx 6.54 \times 10^{-7} \, \text{m} \]

5. **Convert to Nanometers**:
Since the question may require the answer in nanometers, convert meters to nanometers (1 m = \(10^9\) nm):
\[ \lambda = 6.54 \times 10^{-7} \, \text{m} = 654 \, \text{nm} \]

### Final Answer:
The wavelength of light is \( \lambda = 654 \, \text{nm} \).