Question

If \(\mathrm{V}_{\mathrm{r}}, \mathrm{V}_{\mathrm{x}}\) and \(\mathrm{V}_{\mathrm{m}}\) are the velocity of the \(\gamma\) rays, \(\mathrm{x}\) rays, micro waves respectively in space, then (A) \(\mathrm{V}_{\gamma}<\mathrm{V}_{\mathrm{x}}<\mathrm{V}_{\mathrm{m}}\) (B) \(\mathrm{V}_{\mathrm{r}}=\mathrm{V}_{\mathrm{x}}=\mathrm{V}_{\mathrm{m}}\) (C) \(\mathrm{V}_{\mathrm{r}}^{\prime}>\mathrm{V}_{\mathrm{x}}>\mathrm{V}_{\mathrm{m}}\) (D) \(\mathrm{V}_{\mathrm{r}}>\mathrm{V}_{\mathrm{x}}<\mathrm{V}_{\mathrm{m}}\)

Short answer

The short answer is: All types of electromagnetic waves, including gamma rays, X-rays, and microwaves, travel at the speed of light (\(c\)) in a vacuum. Therefore, their velocities are equal: \(V_r = V_x = V_m\). So, the correct answer is (B) \(\mathrm{V}_{\mathrm{r}}=\mathrm{V}_{\mathrm{x}}=\mathrm{V}_{\mathrm{m}}\).

Step-by-step solution

Identify the properties of electromagnetic waves

The main property we should consider is that all electromagnetic waves, including gamma rays, X-rays, and microwaves, travel at the speed of light (\(c\)) in a vacuum, such as outer space.

Compare the velocities of each type of electromagnetic wave

Since gamma rays (\(V_r\)), X-rays (\(V_x\)), and microwaves (\(V_m\)) are all types of electromagnetic waves, they all propagate at the speed of light (\(c\)) in a vacuum. Therefore, we can conclude that their velocities are equal: \(V_r = V_x = V_m\).

Determine the correct answer

Comparing the velocities of each type of electromagnetic wave, we found that \(V_r = V_x = V_m\). Therefore, the correct answer is (B) \(\mathrm{V}_{\mathrm{r}}=\mathrm{V}_{\mathrm{x}}=\mathrm{V}_{\mathrm{m}}\).