Problem 2115 - JEE Physics

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) \(\mathrm{V}_{\mathrm{r}}>\mathrm{V}_{\mathrm{x}}<\mathrm{V}_{\mathrm{m}}\)

Step-by-Step Solution

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 1: 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.

Step 2: 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: \(V_r = V_x = V_m\).

Step 3: 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) \(\mathrm{V}_{\mathrm{r}}=\mathrm{V}_{\mathrm{x}}=\mathrm{V}_{\mathrm{m}}\).

Key Concepts

Speed of Light

In the realm of physics, the speed of light is one of the most fundamental constants. It is denoted by the symbol \(c\) and treated as a universal speed limit for anything that travels through space in a vacuum. Light travels at an astonishing speed of approximately \(3 \times 10^8\) meters per second (or 300,000 kilometers per second).
This speed is remarkably fast and is the maximum speed at which information or matter can travel, according to Einstein's theory of relativity.

• Speed of light \(c\) is exactly equal in any inertial frame of reference.
• All electromagnetic radiation, whether it is visible light or other waves, travels at this speed in a vacuum.

Understanding the speed of light is essential in comprehending how electromagnetic waves, such as gamma rays, X-rays, and microwaves, behave and how they are capable of transferring energy across vast distances instantaneously in space.

Gamma Rays

Gamma rays are a form of electromagnetic radiation with the shortest wavelength and highest energy. These rays are produced by the radioactive decay of atomic nuclei and can also occur in extreme cosmic events.
Having energy levels much higher than other electromagnetic waves, gamma rays can penetrate materials more effectively than other types and pose biological risks.

• They have wavelengths less than 0.01 nanometers (extremely short).
• Emitted during nuclear reactions and certain astronomical phenomena.

Despite their potential dangers, gamma rays have beneficial applications, such as in the sterilization of medical equipment and cancer treatment, where they target and destroy cancerous cells.

X-rays

X-rays are another type of electromagnetic wave with higher energy and shorter wavelengths than visible light, but they are not as powerful as gamma rays.
Commonly used in the medical field, X-rays are vital diagnostic tools enabling doctors to view inside the human body without the need for invasive procedures.

• Wavelengths range from about 0.01 to 10 nanometers.
• Used in radiography and computed tomography (CT) scans.

X-rays work by passing through the body, with the capability to generate images of bones and various organs based on the absorption of the rays by different tissues and materials.

Microwaves

Microwaves fall on the electromagnetic spectrum between infrared radiation and radio waves, characterized by relatively longer wavelengths ranging from about 1 millimeter to 1 meter.
Widely recognized for their use in microwave ovens, these waves cause water molecules in food to vibrate, producing heat and cooking the food.

• Wavelengths extend from 1 millimeter to 1 meter.
• Used in various technologies such as radar and communication devices.

In addition to their role in heating food, microwaves are crucial in satellite communications and radar technology, as they can penetrate clouds, rain, and smoke, ensuring effective data transmission and navigation.