The Vividh Bharati Station of All india Radio, Delhi broadcasts on a frequency of `1368 kHz` (kilo hertz). Calculate the wavelength and wave number of the electronetic radiation emitted by the transmitter.

Explanation

To solve the problem of calculating the wavelength and wave number of the electromagnetic radiation emitted by the Vividh Bharati Station broadcasting at a frequency of 1368 kHz, we will follow these steps:

### Step 1: Convert the Frequency from kHz to Hz
The frequency given is in kilohertz (kHz), and we need to convert it to hertz (Hz) for our calculations.

\[ \text{Frequency} (f) = 1368 \, \text{kHz} = 1368 \times 10^3 \, \text{Hz} = 1.368 \times 10^6 \, \text{Hz} \]

### Step 2: Use the Speed of Light to Calculate Wavelength
The relationship between the speed of light (c), frequency (f), and wavelength (λ) is given by the formula:

\[ c = f \times \lambda \]

We can rearrange this formula to solve for wavelength (λ):

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

Where:
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)
- \( f \) = \( 1.368 \times 10^6 \, \text{Hz} \)

Now substituting the values:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{1.368 \times 10^6 \, \text{Hz}} \approx 219.0 \, \text{meters} \]

### Step 3: Calculate the Wave Number
The wave number (ν̅) is defined as the reciprocal of the wavelength:

\[ \nu̅ = \frac{1}{\lambda} \]

Substituting the value of λ we found:

\[ \nu̅ = \frac{1}{219.0 \, \text{m}} \approx 4.57 \times 10^{-3} \, \text{m}^{-1} \]

To express this in a more standard form, we can convert it to centimeters:

\[ \nu̅ \approx 4.57 \times 10^{3} \, \text{m}^{-1} \]

### Final Answers
- Wavelength (λ) = 219.0 meters
- Wave number (ν̅) = 4.57 × 10³ m⁻¹

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