If λ=`9.7xx10^-8m`, what is frequency of photon ?

Options

A. `3.1xx10^(15)Hz`
B. `3.1xx10^(18)Hz`
C. `9.1xx10^(15)Hz`
D. `9.1xx10^(18)Hz`

Explanation

To find the frequency of a photon given its wavelength, we can use the formula:

\[ \nu = \frac{C}{\lambda} \]

where:
- \(\nu\) is the frequency,
- \(C\) is the speed of light (approximately \(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength.

### Step-by-step Solution:

1. **Identify the given values:**
- Wavelength, \(\lambda = 9.7 \times 10^{-8} \, \text{m}\)
- Speed of light, \(C = 3 \times 10^8 \, \text{m/s}\)

2. **Substitute the values into the frequency formula:**
\[ \nu = \frac{C}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{9.7 \times 10^{-8} \, \text{m}} \]

3. **Perform the division:**
- First, calculate the numerical part:
\[ \frac{3}{9.7} \approx 0.3093 \]
- Now, handle the powers of ten:
\[ 10^8 \div 10^{-8} = 10^{8 - (-8)} = 10^{8 + 8} = 10^{16} \]

4. **Combine the results:**
\[ \nu \approx 0.3093 \times 10^{16} \, \text{Hz} = 3.093 \times 10^{15} \, \text{Hz} \]
- For simplification, we can round this to:
\[ \nu \approx 3.1 \times 10^{15} \, \text{Hz} \]

5. **Final Answer:**
The frequency of the photon is approximately \(3.1 \times 10^{15} \, \text{Hz}\).