Calculate the wavelength of radio waves associated with frequency of `1 xx 10^5 M Hz.`

Explanation

To calculate the wavelength of radio waves associated with a frequency of \(1 \times 10^5 \, \text{MHz}\), we can use the relationship between wavelength (\(\lambda\)) and frequency (\(f\)), which is given by the equation:

\[ c = \lambda \cdot f \]

where:
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters,
- \(f\) is the frequency in hertz (Hz).

### Step 1: Convert frequency from megahertz to hertz
First, we need to convert the frequency from megahertz (MHz) to hertz (Hz). We know that:

\[ 1 \, \text{MHz} = 10^6 \, \text{Hz} \]

Thus,

\[ 1 \times 10^5 \, \text{MHz} = 1 \times 10^5 \times 10^6 \, \text{Hz} = 1 \times 10^{11} \, \text{Hz} \]

### Step 2: Use the speed of light to find the wavelength
Now that we have the frequency in hertz, we can rearrange the equation \(c = \lambda \cdot f\) to solve for wavelength (\(\lambda\)):

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

Substituting the values:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{1 \times 10^{11} \, \text{Hz}} \]

### Step 3: Calculate the wavelength
Now we perform the division:

\[ \lambda = 3 \times 10^8 \div 1 \times 10^{11} = 3 \times 10^{-3} \, \text{m} \]

### Step 4: Final answer
Thus, the wavelength of the radio waves associated with a frequency of \(1 \times 10^5 \, \text{MHz}\) is:

\[ \lambda = 3 \times 10^{-3} \, \text{m} \quad \text{or} \quad 3 \, \text{mm} \]

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