The wavelength of a spectral line of cesium is 460 nm. Calculate the frequency of the line.

Explanation

To calculate the frequency of a spectral line of cesium with a given wavelength of 460 nm, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
- The given wavelength is 460 nm (nanometers).
- To convert nanometers to meters, we use the conversion factor:
\[ 1 \text{ nm} = 10^{-9} \text{ m} \]
- Therefore,
\[ \lambda = 460 \text{ nm} = 460 \times 10^{-9} \text{ m} = 4.60 \times 10^{-7} \text{ m} \]

2. **Use the Speed of Light Formula**:
- The relationship between the speed of light (c), wavelength (λ), and frequency (ν) is given by the equation:
\[ c = \lambda \cdot \nu \]
- Rearranging this formula to solve for frequency (ν):
\[ \nu = \frac{c}{\lambda} \]

3. **Substitute Known Values**:
- The speed of light (c) is approximately \(3 \times 10^8 \text{ m/s}\).
- Now, substitute the values into the frequency formula:
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{4.60 \times 10^{-7} \text{ m}} \]

4. **Perform the Calculation**:
- Calculate the frequency:
\[ \nu = \frac{3 \times 10^8}{4.60 \times 10^{-7}} = \frac{3}{4.60} \times 10^{8 + 7} = \frac{3}{4.60} \times 10^{15} \]
- Now calculate \( \frac{3}{4.60} \):
\[ \frac{3}{4.60} \approx 0.652 \]
- Therefore,
\[ \nu \approx 0.652 \times 10^{15} \text{ Hz} = 6.52 \times 10^{14} \text{ Hz} \]

5. **Final Result**:
- The frequency of the spectral line of cesium is approximately:
\[ \nu \approx 6.52 \times 10^{14} \text{ Hz} \]