Question

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

Short answer

De Broglie waves do not travel with the speed of light.

Step-by-step solution

Understanding Speed of Light

First, we need to understand that the speed of light is constant and is approximately \(3 imes 10^8\) meters per second in a vacuum. Light waves, including all types of electromagnetic waves such as X-rays and Gamma rays, travel at this speed in a vacuum.

Understanding De Broglie Waves

De Broglie waves are not electromagnetic waves; they represent the wave nature of particles. According to De Broglie's hypothesis, a moving particle has a wavelength given by \(\lambda = \frac{h}{p}\), where \(\lambda\) is the wavelength, \(h\) is Planck's constant, and \(p\) is the momentum. These waves are associated with particles like electrons that do not necessarily travel at the speed of light.

Analyzing Options

Given the options: (a) De Broglie waves, (b) X-rays, and (c) Gamma rays, we know that (b) and (c) are electromagnetic waves and therefore travel at the speed of light. However, as discussed in Step 2, De Broglie waves are associated with particles and do not travel at the speed of light unless the particle is massless, like a photon.

Choosing the Correct Option

Since De Broglie waves are associated with particles, which in general do not travel at the speed of light, the correct answer is that De Broglie waves do not travel with the speed of light.

Key concepts

Speed of Light

The speed of light is a fundamental constant in physics, symbolized as \( c \), and is the maximum speed at which all energy, matter, and information in the universe can travel. It is approximately equal to \( 3 \times 10^8 \) meters per second in a vacuum. Understanding this speed is crucial because it sets a universal speed limit. Whether you’re talking about light from the sun or electromagnetic waves like X-rays and gamma rays, they all travel at this speed in a vacuum. This principle is a cornerstone of Einstein's theory of relativity, which describes how space and time are interconnected

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• The speed of light is the same for all observers, regardless of the motion of light source or observer.
• Nothing with mass can reach the speed of light. Only massless particles, like photons, can travel at this speed.

In various mediums, light slows down; however, its speed in a vacuum remains constant.

De Broglie Waves

De Broglie waves are a concept that represents the wave nature of particles and were introduced by the physicist Louis de Broglie. According to De Broglie's hypothesis, any moving particle, such as an electron, can exhibit wave-like properties. The wavelength of a particle is given by the equation \( \lambda = \frac{h}{p} \), where \( \lambda \) is the wavelength, \( h \) is Planck’s constant, and \( p \) is the momentum of the particle

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• De Broglie waves are different from electromagnetic waves as they are associated with material particles rather than energy.
• These waves reveal the dual nature of matter, demonstrating its particle and wave characteristics.

The concept of De Broglie waves led to the development of quantum mechanics, allowing scientists to better understand atomic and subatomic particles.

Electromagnetic Waves

Electromagnetic waves are waves that can travel through the vacuum of outer space. They are created as a result of vibrations between an electric field and a magnetic field. These waves are a fundamental phenomenon of nature, forming the electromagnetic spectrum, which includes gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, and radio waves

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• All electromagnetic waves travel at the speed of light in a vacuum.
• They do not require a medium to travel, unlike mechanical waves which do.

Electromagnetic waves vary in their wavelength and frequency. For example, visible light has a smaller wavelength than radio waves, but they both travel at the same speed in a vacuum.

X-rays

X-rays are a form of electromagnetic radiation with wavelengths much shorter than that of visible light. Discovered by Wilhelm Röntgen, X-rays are commonly used in medical imaging to view the inside of the human body. These rays have the ability to penetrate various materials to different extents, which makes them invaluable in medicine and industry

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• X-rays travel at the speed of light in a vacuum, just like all other electromagnetic waves.
• They have higher energy than visible light, which allows them to pass through objects such as bones and tissues.

Despite their benefits, exposure to X-rays needs to be controlled as they can be harmful due to their high energy levels.

Gamma Rays

Gamma rays are the highest-energy form of electromagnetic radiation and have the shortest wavelength in the electromagnetic spectrum. They are produced by the hottest and most energetic objects in the universe, such as neutron stars and supernova explosions. On Earth, they can be created by nuclear reactions

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• Gamma rays are used in medical treatments, such as cancer radiotherapy, due to their ability to kill cancer cells.
• Like other electromagnetic waves, they travel at the speed of light in a vacuum.

Their high energy allows them to penetrate most materials, which is why heavy lead shielding is used when working with gamma rays to protect human health.