Problem 117 - 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 velocity of thermal radiation is approximately \(3 \times 10^{8} \ \mathrm{ms}^{-1}\). Thus, the answer is (c).

Step 1: Identify the Nature of Thermal Radiation

Thermal radiation is a form of electromagnetic radiation, which includes visible light, infrared, and other wavelengths. This helps us link thermal radiation to the velocity of electromagnetic waves.

Step 2: Recall the Speed of Electromagnetic Waves

Electromagnetic waves travel at a constant speed in a vacuum, known as the speed of light. Hence, the velocity of thermal radiation is the same as the speed of light, which is approximately \(3 \times 10^{8} \ \mathrm{ms}^{-1} \).

Step 3: Match the Velocity with Given Options

Among the given options, \(3 \times 10^{8} \ \mathrm{ms}^{-1} \) matches the known speed of electromagnetic waves in a vacuum. Thus, the correct answer is option (c).

Key Concepts

Speed of Light

The speed of light is a fundamental constant in physics, representing how fast light travels in a vacuum. This speed is approximately \(3 \times 10^{8} \ \mathrm{ms}^{-1}\). This high velocity is shared by all types of electromagnetic waves, not just visible light.
Light travels so fast that it can circle the Earth more than seven times in just one second!

• The speed of light is crucial for various technological advancements, such as GPS and communication satellites.
• It serves as a cosmic speed limit, with nothing able to travel faster through a vacuum naturally.

Understanding this speed is essential for comprehending phenomena related to astronomy, optics, and electromagnetism.

Electromagnetic Waves

Electromagnetic waves are waves of energy associated with electric and magnetic fields. They travel through space at the speed of light, which is why thermal radiation, a type of electromagnetic wave, also travels at \(3 \times 10^{8} \ \mathrm{ms}^{-1}\).
These waves can vary in wavelength and frequency, forming the electromagnetic spectrum.

• Types of electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
• Each type has unique properties and applications in daily life, such as radio for communication and X-rays for medical imaging.

Electromagnetic waves can travel through the vacuum of space, unlike sound waves that need a medium.

Nature of Thermal Radiation

Thermal radiation is energy emitted by matter due to its temperature in the form of electromagnetic waves. Even the warmth you feel from the sun is thermal radiation!
Because it's a type of electromagnetic radiation, it shares properties with other electromagnetic waves, including traveling at the speed of light.

• Unlike conduction and convection that require a medium, thermal radiation can pass through a vacuum, such as space.
• All objects emit thermal radiation, but as an object's temperature rises, the amount and energy of emitted radiation increases.

This concept helps us understand energy transfer mechanisms and the behavior of objects at different temperatures.