Let's analyze the characteristics of photons generated by a microwave oven and an X-ray machine in terms of frequency, energy, and wavelength.
### Frequency:
Frequency is directly related to the energy of the photon; higher frequency means higher energy. X-rays are known to have a much higher frequency than microwaves. Therefore, the photon with the greater frequency is the X-ray.
### Energy:
The energy of a photon is directly proportional to its frequency. Since X-rays have a higher frequency compared to microwaves, they also have greater energy. Thus, X-rays have greater energy.
### Wavelength:
The wavelength is inversely proportional to the frequency of the photon. Higher frequency photons have shorter wavelengths. Since microwaves have a lower frequency compared to X-rays, they have a longer wavelength. Therefore, microwaves have a greater wavelength.
Based on this analysis:
- The photon with the greater frequency is the X-ray.
- The photon with the greater energy is the X-ray.
- The photon with the greater wavelength is the microwave.
Thus, the correct answer is:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline & Greater Frequency & Greater Energy & Greater Wavelength \\
\hline b. & X-ray & X-ray & Microwave \\
\hline
\end{tabular}
\][/tex]
So the answer is b.
