Problem 116 - Master Resource Book in JEE Main Physics

Question

The thermal radiation from a hot body travels with a velocity of (a) \(330 \mathrm{~ms}^{-1}\) (b) \(2 \times 10^{8} \mathrm{~ms}^{-1}\) (c) \(3 \times 10^{8} \mathrm{~ms}^{-1}\) (d) \(230 \times 10^{8} \mathrm{~ms}^{-1}\)

Step-by-Step Solution

Answer

The correct answer is (c) \(3 \times 10^8 \mathrm{~ms}^{-1}\).

Step 1: Understanding Thermal Radiation

Thermal radiation is a form of electromagnetic radiation emitted by all objects with a temperature above absolute zero. It travels as waves and does not require a medium for propagation.

Step 2: Speed of Electromagnetic Waves

All forms of electromagnetic radiation, including thermal radiation (infrared radiation), travel at the same speed in a vacuum, which is the speed of light.

Step 3: Identify the Speed of Light

The speed of light in a vacuum is approximately \(3 \times 10^8 \mathrm{~ms}^{-1}\). This is a fundamental constant of nature.

Step 4: Selecting the Correct Option

Given the options: (a) \(330 \mathrm{~ms}^{-1}\) (b) \(2 \times 10^8 \mathrm{~ms}^{-1}\) (c) \(3 \times 10^8 \mathrm{~ms}^{-1}\) (d) \(230 \times 10^8 \mathrm{~ms}^{-1}\),choose the one that matches the speed of electromagnetic waves, which is (c) \(3 \times 10^8 \mathrm{~ms}^{-1}\).

Key Concepts

Electromagnetic Waves

Electromagnetic waves are fascinating phenomena that occur when electric and magnetic fields interact. These are waves that can travel through the vacuum of space. Unlike sound waves, which need a medium like air or water to travel, electromagnetic waves can move through empty space. This makes them unique and fundamental to many processes in the universe.

They cover a wide range of types, known as the electromagnetic spectrum, which includes:

• Radio waves: Used for long-distance communication.
• Microwaves: Found in microwave ovens and radar technology.
• Infrared radiation: Often experienced as heat.
• Visible light: The only part of the spectrum visible to the human eye.
• Ultraviolet light: Can cause sunburn.
• X-rays: Used in medicine to view inside the body.
• Gamma rays: Emitted by radioactive materials and certain cosmic phenomena.

Electromagnetic waves play a crucial role in modern life, from the light we see to the radiation used in medical technology.

Speed of Light

The speed of light is one of the most important constants in physics. It defines the speed at which all electromagnetic waves, including visible light, travel through a vacuum. This speed is about \[3 \times 10^8 \mathrm{~ms}^{-1}.\] This is incredibly fast, enabling light to travel vast distances across space in what seems like no time at all.

The speed of light is vital not only in physics but also in various technologies and applications, such as:

• Communications: Light speed underpins technologies like fiber optics.
• Astronomy: By measuring how light from distant objects takes to reach us, we can calculate the universe's size and age.
• GPS: Accounts for light speed to provide accurate positioning information.

Understanding light speed is fundamental to the theory of relativity, where it acts as the ultimate speed limit in the universe.

Infrared Radiation

Infrared radiation is an essential part of the electromagnetic spectrum. Though invisible to the human eye, it is commonly experienced as heat. This form of radiation can be emitted by all objects that possess a temperature above absolute zero. This property makes it critical in various practical applications.

Some common uses of infrared radiation include:

• Night-vision equipment: Detects heat emitted by objects to "see" in the dark.
• Thermal imaging: Used in medical diagnostics and building inspections.
• Remote controls: Operate TVs and other devices by sending infrared signals.
• Astronomy: Helps astronomers see objects obscured by dust in space, which is invisible in other wavelengths.

In scientific research and technology, understanding infrared radiation allows us to utilize heat detection and management in innovative ways. This radiation type highlights the incredible versatility of electromagnetic waves in daily life.