Calculate the frequency and wave number of radiations with wavelength 480 nm.

Explanation

To calculate the frequency and wave number of radiation with a wavelength of 480 nm, we will follow these steps:

### Step 1: Convert Wavelength to Meters
The given wavelength is 480 nm (nanometers). We need to convert this to meters.

\[ \text{Wavelength} (\lambda) = 480 \, \text{nm} = 480 \times 10^{-9} \, \text{m} \]

### Step 2: Use the Speed of Light to Calculate Frequency
The speed of light (c) is approximately \(3 \times 10^8 \, \text{m/s}\). The relationship between speed, frequency (ν), and wavelength (λ) is given by the equation:

\[ c = \nu \lambda \]

Rearranging this formula to solve for frequency gives us:

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

Substituting the values we have:

\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{480 \times 10^{-9} \, \text{m}} \]

### Step 3: Calculate Frequency
Now we perform the calculation:

\[ \nu = \frac{3 \times 10^8}{480 \times 10^{-9}} = \frac{3 \times 10^8}{4.8 \times 10^{-7}} = 6.25 \times 10^{14} \, \text{Hz} \]

### Step 4: Calculate Wave Number
The wave number (denoted as \( \tilde{\nu} \)) is defined as the reciprocal of the wavelength:

\[ \tilde{\nu} = \frac{1}{\lambda} \]

Substituting the wavelength in meters:

\[ \tilde{\nu} = \frac{1}{480 \times 10^{-9} \, \text{m}} = \frac{1}{4.8 \times 10^{-7}} \approx 2.083 \times 10^6 \, \text{m}^{-1} \]

### Final Answers
- **Frequency (ν)**: \(6.25 \times 10^{14} \, \text{Hz}\)
- **Wave Number (\( \tilde{\nu} \))**: \(2.083 \times 10^6 \, \text{m}^{-1}\)

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