In electromagnetic spectrum, the frequencies of `gamma`-rays and `X-`rays and ultraviolet rays are denoted by `n_(1),n_(2)` and `n_(3)` respectively, then

Options

A. `n_(1) gt n_(2) gt n_(3)`
B. `n_(1) lt n_(2) lt n_(3)`
C. `n_(1) gt n_(2) lt n_(3)`
D. `n_(1) lt n_(2) gt n_(3)`

Explanation

To solve the problem, we need to compare the frequencies of gamma rays, X-rays, and ultraviolet rays in the electromagnetic spectrum. We denote the frequencies as follows:

- \( n_1 \): frequency of gamma rays
- \( n_2 \): frequency of X-rays
- \( n_3 \): frequency of ultraviolet rays

### Step 1: Understand the relationship between wavelength and frequency
In the electromagnetic spectrum, the relationship between wavelength (\( \lambda \)) and frequency (\( \nu \)) is given by the equation:
\[ c = \lambda \nu \]
where \( c \) is the speed of light. This implies that:
\[ \nu = \frac{c}{\lambda} \]
Thus, frequency is inversely proportional to wavelength.

### Step 2: Order the wavelengths of the electromagnetic spectrum
From the electromagnetic spectrum, we know the order of wavelengths for these types of radiation:
- Gamma rays have the shortest wavelength.
- X-rays have a longer wavelength than gamma rays but shorter than ultraviolet rays.
- Ultraviolet rays have the longest wavelength among the three.

This can be summarized as:
\[ \lambda_{\text{gamma}} < \lambda_{\text{x-ray}} < \lambda_{\text{ultraviolet}} \]

### Step 3: Determine the order of frequencies
Since frequency is inversely proportional to wavelength, the order of frequencies will be the opposite of the order of wavelengths:
- Since gamma rays have the shortest wavelength, they have the highest frequency.
- X-rays have a higher frequency than ultraviolet rays but lower than gamma rays.
- Ultraviolet rays have the longest wavelength, hence the lowest frequency.

Thus, we can write:
\[ n_1 > n_2 > n_3 \]

### Conclusion
The correct relationship among the frequencies is:
\[ n_1 > n_2 > n_3 \]

### Final Answer
The answer is \( n_1 > n_2 > n_3 \).

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