Calculate the wavelength in meters of electromagnetic radiation that has a frequency of 1.02 × 10⁸ s⁻¹. (c = 3.00 X 10⁸ m/s)

To calculate the wavelength (\(\lambda\)) of electromagnetic radiation, we can use the equation:

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

Where:
- \(\lambda\) is the wavelength (in meters),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(f\) is the frequency of the radiation.

Given:
\[
f = 1.02 \times 10^8 \, \text{s}^{-1}
\]

Substitute the given values into the equation:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{1.02 \times 10^8 \, \text{s}^{-1}}
\]

Now, let's calculate:

\[
\lambda = 2.94 \, \text{m}
\]

Thus, the wavelength of the electromagnetic radiation is **2.94 meters**.

Would you like more details on the calculation? Here are 5 related questions to deepen your understanding:

1. What is the relationship between wavelength and frequency in electromagnetic radiation?
2. How does the speed of light affect the wavelength of radiation at different frequencies?
3. What type of electromagnetic radiation has a frequency of \(1.02 \times 10^8 \, \text{s}^{-1}\)?
4. How would the wavelength change if the frequency were doubled?
5. Can wavelength be measured directly, or is it always calculated from frequency?

**Tip:** Frequency and wavelength are inversely related, meaning that higher frequencies correspond to shorter wavelengths, and vice versa.

Learn how to calculate the wavelength of electromagnetic radiation given a frequency of 1.02 × 10⁸ s⁻¹. This solution demonstrates the application of the wavelength formula λ = c / f, where c is the speed of light, to solve real-world physics problems. Suitable for students in Grades 9-12.

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