The wavelength of a beam of light is `25.0 mu m`. What is its frequency and wave number ?

Explanation

To find the frequency and wave number of a beam of light with a wavelength of \( 25.0 \, \mu m \), we can follow these steps:

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

\[ \text{Wavelength} (\lambda) = 25.0 \, \mu m = 25.0 \times 10^{-6} \, m \]

### Step 2: Calculate Frequency
The frequency (\( f \)) of light can be calculated using the formula:

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

where:
- \( c \) is the speed of light, approximately \( 3.0 \times 10^8 \, m/s \)
- \( \lambda \) is the wavelength in meters

Substituting the values:

\[ f = \frac{3.0 \times 10^8 \, m/s}{25.0 \times 10^{-6} \, m} \]

Calculating this gives:

\[ f = \frac{3.0 \times 10^8}{25.0 \times 10^{-6}} = 1.2 \times 10^{13} \, Hz \]

### Step 3: Calculate Wave Number
The wave number (\( \bar{\nu} \)) is defined as the reciprocal of the wavelength:

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

To find the wave number in meters, we can use the wavelength in meters:

\[ \bar{\nu} = \frac{1}{25.0 \times 10^{-6} \, m} \]

Calculating this gives:

\[ \bar{\nu} = 4.0 \times 10^4 \, m^{-1} \]

### Final Results
- Frequency (\( f \)): \( 1.2 \times 10^{13} \, Hz \)
- Wave number (\( \bar{\nu} \)): \( 4.0 \times 10^4 \, m^{-1} \)

---