Question

The frequencies of \(\mathrm{x}\) rays, \(\gamma\) rays and ultraviolet rays are respectively \(\mathrm{p}, \mathrm{q}\) and \(\mathrm{r}\) then (A) \(pr\) (B) \(p>q, q>r\) (C) \(p>q, q

Short answer

The correct statement is (A) \(pr\), which represents the relationships between the frequencies of x-rays, gamma rays, and ultraviolet rays according to the electromagnetic spectrum order.

Step-by-step solution

Recall the electromagnetic spectrum order

The electromagnetic spectrum is a continuous range of wavelengths and frequencies of electromagnetic waves. It can be remembered by the following order, from the lowest frequency (longest wavelength) to the highest frequency (shortest wavelength): Radio waves → Microwaves → Infrared → Visible Light → Ultraviolet → X-rays → Gamma rays

Compare the frequencies of x-rays, gamma rays, and ultraviolet

From the order of the electromagnetic spectrum, we can see the position of each type of ray: - X-rays: Higher frequency than ultraviolet but lower frequency than gamma rays. - Gamma rays: Highest frequency. - Ultraviolet rays: Lower frequency than x-rays and gamma rays. Now, let's compare their frequencies: - p (x-rays): Based on the electromagnetic spectrum order, the frequency of x-rays is higher than ultraviolet and lower than gamma rays; therefore, \(p > r\) and \(p < q\). - q (gamma rays): Being the highest frequency, gamma rays have a frequency greater than x-rays and ultraviolet rays; thus, \(q > p\) and \(q > r\). - r (ultraviolet rays): Having the lowest frequency, the frequency of ultraviolet rays is lower than x-rays and gamma rays; so, \(r < p\) and \(r < q\).

Identify the correct statement

With the comparisons in Step 2, we can find the correct statement among the options given. (A) \(p < q, q > r\): This statement corresponds to the relationships we derived in Step 2. Therefore, \textbf{option A is the correct answer}. (B) \(p > q, q > r\): This statement is incorrect because gamma rays (q) have a higher frequency than x-rays (p). (C) \(p > q, q < r\): This statement is incorrect because gamma rays (q) have the highest frequency among the three types of rays. (D) \(p < q, q < r\): This statement is incorrect because ultraviolet rays (r) have a lower frequency than x-rays (p) and gamma rays (q).