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

The objective is to determine the ratio between the shortest wavelength of radio waves and the longest wavelength of gamma waves. The provided values are as follows:

1. Shortest Wavelength of Radio Waves:

The shortest wavelength for radio waves is approximately \( 0.1 \, \text{m} \). This value is assigned to:

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

2. Longest Wavelength of Gamma Waves:

The longest wavelength for gamma rays is approximately \( 10^{-12} \, \text{m} \). This value is assigned to:

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

3. Ratio of Wavelengths:

The ratio is calculated by dividing the shortest radio wave wavelength by the longest gamma wave wavelength:

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

Substituting the given values yields:

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

4. Conclusion:

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