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

(a) De-Broglie waves do not travel with the speed of light.

Step 1: Understanding Speed of Light

Light travels at a speed of approximately 299,792,458 meters per second in a vacuum. This speed is denoted as "c" and is the maximum speed at which all massless particles and associated fields, including electromagnetic radiation such as light, can travel.

Step 2: Analyzing De-Broglie Waves

De-Broglie waves are associated with matter, such as electrons and other particles that have mass. The speed of De-Broglie waves depends on the momentum and energy of the particles, and they do not necessarily travel at the speed of light.

Step 3: Examining X-rays and Gamma Rays

X-rays and Gamma rays are forms of electromagnetic radiation. Since all electromagnetic waves travel at the speed of light in a vacuum, both X-rays and Gamma rays travel at this speed.

Step 4: Conclusion

Among the given options, De-Broglie waves are associated with particles having mass and do not travel at the speed of light, unlike X-rays and Gamma rays which do.

Key Concepts

De-Broglie waves

De-Broglie waves are fundamental to understanding the quantum nature of matter. Unlike typical electromagnetic waves, De-Broglie waves are associated with particles that have mass, such as electrons. This means they can behave both like particles and waves, a dual nature central to quantum mechanics.

• The wave aspect arises from the wave-particle duality principle, which implies particles can demonstrate wave-like behavior under certain conditions.
• The wavelength of a De-Broglie wave is determined by the momentum of the particle, given by the formula \( \lambda = \frac{h}{p} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant, and \( p \) is momentum.

De-Broglie waves do not travel at the speed of light, instead, their velocity is linked to the speed and mass of the particle. Understanding these waves is essential for grasping topics like electron diffraction and quantum mechanics.

Electromagnetic radiation

Electromagnetic radiation encompasses a vast range of wavelengths and frequencies, part of what is known as the electromagnetic spectrum.

• This spectrum includes visible light as well as invisible waves like radio waves, microwaves, X-rays, and Gamma rays.
• All forms of electromagnetic radiation travel at the speed of light \( c = 299,792,458 \) meters per second in a vacuum.

What sets electromagnetic radiation apart is that it consists of oscillating electric and magnetic fields that travel through space. Despite their varied applications and appearances, from communication technologies to medical imaging, all electromagnetic waves share this fundamental property of traveling at light speed in a vacuum.

X-rays

X-rays are a form of electromagnetic radiation, known for their ability to pass through most objects, including the human body. They occupy a higher energy range on the electromagnetic spectrum, just beyond ultraviolet light.

• X-rays play a crucial role in medical imaging, helping doctors view the inside of the human body with procedures like X-ray radiography.
• They are also used in security, materials science, and astronomy.

Since X-rays are a subset of electromagnetic waves, they travel at the speed of light in a vacuum. This rapid speed, coupled with their penetrating power, makes them extremely useful both in medicine and industry.

Gamma rays

Gamma rays are the most energetic form of electromagnetic radiation. They arise in processes such as radioactive decay and nuclear reactions, carrying significant amounts of energy.

• Gamma rays are used in medical treatments, such as in cancer radiotherapy, due to their ability to kill living cells.
• They are also crucial in scientific research, helping us understand cosmic phenomena through gamma-ray astronomy.

Like all electromagnetic waves, gamma rays travel at the speed of light in a vacuum. Their incredible energy allows them to penetrate most materials, which is why they are heavily regulated and used with caution in various applications.