Calculate the frequency (v) and wave number `(bar(v))` of the yellow light with a wavelength of 580 nm emitted from sodium lamp.

Answer

To solve the problem of calculating the frequency (ν) and wave number (ṽ) of yellow light with a wavelength of 580 nm emitted from a sodium lamp, we can follow these steps:

### Step 1: Convert Wavelength to Meters
The wavelength (λ) is given in nanometers (nm). We need to convert it to meters (m) for our calculations.

\[ \lambda = 580 \, \text{nm} = 580 \times 10^{-9} \, \text{m} \]

### Step 2: Calculate the Wave Number (ṽ)
The wave number (ṽ) is defined as the reciprocal of the wavelength. It is given by the formula:

\[ \bar{v} = \frac{1}{\lambda} \]

Substituting the value of λ:

\[ \bar{v} = \frac{1}{580 \times 10^{-9}} \, \text{m}^{-1} \]

Calculating this gives:

\[ \bar{v} = \frac{1}{580} \times 10^{9} \approx 1.724 \times 10^{6} \, \text{m}^{-1} \]

### Step 3: Calculate the Frequency (ν)
The frequency (ν) can be calculated using the speed of light (c) and the wavelength (λ) with the formula:

\[ c = \nu \lambda \]

Rearranging this gives:

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

Where the speed of light (c) is approximately \(3 \times 10^{8} \, \text{m/s}\). Substituting the known values:

\[ \nu = \frac{3 \times 10^{8}}{580 \times 10^{-9}} \]

Calculating this gives:

\[ \nu \approx \frac{3 \times 10^{8}}{580 \times 10^{-9}} \approx 5.172 \times 10^{14} \, \text{Hz} \]

### Final Answers
- Wave number (ṽ) = \(1.724 \times 10^{6} \, \text{m}^{-1}\)
- Frequency (ν) = \(5.172 \times 10^{14} \, \text{Hz}\)