Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following do not travel with speed of light? (a) De-Broglie waves (b) X-rays (c) Gamma rays (d) All of these

Step-by-Step Solution

Answer

De-Broglie waves do not travel at the speed of light.

Step 1: Identifying the Nature of Waves

Understand that De-Broglie waves are associated with particles and describe the wave-like behavior of matter, unlike electromagnetic waves like X-rays and Gamma rays.

Step 2: Speed Analysis of Electromagnetic Waves

Recognize that X-rays and Gamma rays are types of electromagnetic radiation and, as such, both travel at the speed of light in a vacuum.

Step 3: Speed Analysis of De-Broglie Waves

Know that De-Broglie waves are not electromagnetic in nature and their speed is related to the momentum of the particle they are associated with, meaning they do not travel at the speed of light.

Step 4: Conclusion Based on Speed Analysis

Conclude that De-Broglie waves do not travel at the speed of light, while X-rays and Gamma rays do.

Key Concepts

De-Broglie Waves

De-Broglie waves are a fascinating aspect of quantum mechanics that help us understand the wave-particle duality of matter. In simple terms, de-Broglie waves suggest that matter can exhibit both wave-like and particle-like properties.
This duality means that objects, such as electrons, which we traditionally think of as particles, can also behave as waves under certain conditions. The concept was introduced by Louis de Broglie in 1924, proposing that every moving particle or object has an associated wave.A key characteristic of these waves is their wavelength \[ \lambda = \frac{h}{p} \]where \( \lambda \) is the wavelength, \( h \) is Planck's constant, and \( p \) is the momentum of the particle.

• Not electromagnetic: Unlike X-rays or gamma rays, de-Broglie waves are not electromagnetic.
• Momentum-based speed: Their speed depends on the momentum of the particle, not the speed of light.

Understanding de-Broglie waves helps us to explain phenomena like electron diffraction in materials, reinforcing the idea that traditional particle-based understandings are only part of the picture.

Electromagnetic Waves

Electromagnetic waves are a type of wave that can travel through the vacuum of space. These waves are formed by the oscillation of electric and magnetic fields that move perpendicular to each other and in the direction of wave propagation. What makes electromagnetic waves special is that they travel at the speed of light, which is approximately 299,792 kilometers per second in a vacuum. Some common examples of electromagnetic waves include visible light, microwaves, and radio waves.

• Speed of light: All electromagnetic waves move at the speed of light in a vacuum.
• Wave spectrum: They form a spectrum, ranging from radio waves with long wavelengths to gamma rays with extremely short wavelengths.

These waves are fundamental in modern technology and science, allowing for the transmission of information across vast distances and enabling technologies like televisions and wireless communication.

X-rays

X-rays are a specific type of electromagnetic wave. They hold a significant place in both scientific research and medical imaging due to their ability to penetrate materials of varying densities. This ability stems from their relatively short wavelength, which allows them to pass through matter more easily than waves with longer wavelengths such as radio waves. X-rays were discovered by Wilhelm Conrad Röntgen in 1895 and are produced when high-energy electrons hit a metal target, causing the emission of X-rays. Due to their nature as electromagnetic radiation:

• Speed of light: X-rays travel at the speed of light in a vacuum.
• Use in imaging: The short wavelength provides high resolution in imaging techniques like X-ray radiography used in medicine.

Their use goes beyond medical imaging, as they are also pivotal in fields such as astronomy and material science to analyze structural properties of materials.

Gamma Rays

Gamma rays are at the extreme end of the electromagnetic spectrum and have the shortest wavelengths and highest frequencies of all electromagnetic waves. They arise from radioactive decay in atomic nuclei as well as from processes occurring in the cosmos, such as supernova explosions. The unique properties of gamma rays make them useful in various scientific and medical applications:

• Highest energy: With their high energy and deep penetrating power, gamma rays are used in medical treatments such as cancer radiotherapy.
• Speed of light: As part of the electromagnetic spectrum, gamma rays travel at the speed of light in a vacuum.

Despite their beneficial uses, gamma rays require careful handling due to their potential harm to living tissues and cellular structures. This duality of gamma rays makes them both a powerful tool and a radiation risk in different contexts.