Questions: Find the wavelength of a radio wave whose frequency is 1.02 × 10^11 Hz.

Solution Steps

The relationship between the wavelength (\(\lambda\)) and frequency (\(f\)) of a wave is given by the equation:

\[ c = \lambda \cdot f \]

where \(c\) is the speed of light in a vacuum, approximately \(3.00 \times 10^8 \, \text{m/s}\).

To find the wavelength, rearrange the formula to solve for \(\lambda\):

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

Substitute the given frequency \(f = 1.02 \times 10^{11} \, \text{Hz}\) and the speed of light \(c = 3.00 \times 10^8 \, \text{m/s}\) into the equation:

\[ \lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{1.02 \times 10^{11} \, \text{Hz}} \]

Perform the division to find the wavelength:

\[ \lambda = \frac{3.00 \times 10^8}{1.02 \times 10^{11}} \approx 2.9412 \times 10^{-3} \, \text{m} \]

Final Answer