To solve the problem regarding the relationship between the frequencies of X-rays, gamma rays, and ultraviolet rays, we can follow these steps:
### Step-by-Step Solution:
1. **Understand the Electromagnetic Spectrum**:
The electromagnetic spectrum is a range of all types of electromagnetic radiation, which includes gamma rays, X-rays, ultraviolet rays, visible light, and more. Each type of radiation has a specific range of wavelengths and frequencies.
2. **Identify the Position of Each Type of Radiation**:
In the electromagnetic spectrum, the order from highest frequency to lowest frequency is:
- Gamma rays (highest frequency)
- X-rays
- Ultraviolet rays (lowest frequency)
3. **Relate Frequency and Wavelength**:
The relationship between frequency (f), wavelength (λ), and the speed of light (v) is given by the equation:
\[
v = f \cdot \lambda
\]
Rearranging this gives:
\[
f = \frac{v}{\lambda}
\]
This means that for a constant speed of light, a shorter wavelength corresponds to a higher frequency.
4. **Determine the Frequencies**:
Since gamma rays have the shortest wavelength, they will have the highest frequency. X-rays have a longer wavelength than gamma rays but a shorter wavelength than ultraviolet rays, which means their frequency is lower than that of gamma rays but higher than that of ultraviolet rays. Ultraviolet rays have the longest wavelength among the three, thus the lowest frequency.
5. **Establish the Relationship**:
Based on the above understanding, we can establish the following relationship:
\[
\text{Frequency of gamma rays (b)} > \text{Frequency of X-rays (a)} > \text{Frequency of ultraviolet rays (c)}
\]
Therefore, we can write:
\[
b > a > c
\]
6. **Conclusion**:
The correct relationship between the frequencies of X-rays, gamma rays, and ultraviolet rays is:
\[
b > a > c
\]
### Final Answer:
The frequencies of gamma rays, X-rays, and ultraviolet rays are related as follows:
\[
b > a > c
\]
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