Question

Estimate the ratio of shortest wavelength of radio waves to the longest wavelength of gamma waves.

Hint:

The ratio of wavelengths in different types of electromagnetic waves can vary widely, with radio waves having much longer wavelengths than gamma rays.

Answer 1

We are tasked with estimating the ratio of the shortest wavelength of radio waves to the longest wavelength of gamma waves. Let's first define the given quantities:

1. Shortest Wavelength of Radio Waves:

The shortest wavelength of radio waves is typically in the range of \( 0.1 \, \text{m} \) (10 cm). Thus, we can take:

\[ \lambda_{\text{radio}} = 0.1 \, \text{m} \]

2. Longest Wavelength of Gamma Waves:

The longest wavelength of gamma rays is typically on the order of \( 10^{-12} \, \text{m} \) (1 picometer). Thus, we can take:

\[ \lambda_{\text{gamma}} = 10^{-12} \, \text{m} \]

3. Ratio of Wavelengths:

The ratio of the shortest wavelength of radio waves to the longest wavelength of gamma waves is given by:

\[ \text{Ratio} = \frac{\lambda_{\text{radio}}}{\lambda_{\text{gamma}}} \]

Substituting the values:

\[ \text{Ratio} = \frac{0.1 \, \text{m}}{10^{-12} \, \text{m}} = 10^{11} \]

4. Conclusion:

The ratio of the shortest wavelength of radio waves to the longest wavelength of gamma waves is \( 10^{11} \), or 100 billion.