Magnetism and magnetic fields Revision Notes

Velocity of Electromagnetic Waves in Different Media (Higher)

Electromagnetic (EM) waves, including visible light, travel at a constant speed, 'c' (approximately 3.0 x 10^8 m/s), only in a vacuum. When EM waves enter a material substance, they interact with the atoms and molecules of that substance. These interactions cause the EM waves to slow down considerably. The precise speed of an EM wave in a material medium is always less than its speed in a vacuum. Different materials affect the speed of EM waves to different extents, depending on their optical density and atomic structure. This variation in velocity is a key factor in many optical phenomena.

Refractive Index and Wave Velocity (Higher)

The refractive index (n) of a material is a measure of how much the speed of an electromagnetic wave is reduced when passing through it, compared to its speed in a vacuum. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v): n = c/v. Since 'c' is the maximum speed, the refractive index 'n' is always greater than or equal to 1. A higher refractive index means that the EM wave travels more slowly in that particular medium. For example, water has a refractive index of about 1.33, meaning light travels 1.33 times slower in water than in a vacuum. Diamonds have a high refractive index (around 2.42), indicating a significant slowing of light.

Refraction as a Consequence of Velocity Change (Higher)

Refraction is the phenomenon where electromagnetic waves, such as light, change direction as they pass from one medium to another. This bending occurs because of the change in the wave's velocity when it enters a new medium. If a wavefront encounters the boundary between two media at an angle, one part of the wavefront will enter the new medium and slow down (or speed up) before the other part. This differential change in speed across the wavefront causes the wave to pivot, resulting in a change in its direction of travel. Snell's Law quantitatively describes the relationship between the angles of incidence and refraction, and the refractive indices (and thus, velocities) of the two media.

Effects Caused by Velocity Differences (Higher)

The change in the velocity of electromagnetic waves in different substances leads to several observable effects. Refraction is fundamental to the operation of lenses in spectacles, cameras, and telescopes, where light is precisely bent to form images. It also explains why objects underwater appear shallower than they are, due to light rays bending away from the normal as they exit the water into the air. Prisms disperse white light into its constituent colours because different wavelengths (colours) of light have slightly different speeds in the prism material, causing them to refract at slightly different angles. Total internal reflection, used in fibre optics, also relies on this principle, as light travels from a denser medium to a less dense medium at a large enough angle to be entirely reflected internally.

Balancing Nuclear Equations

Nuclear equations represent radioactive decay and must be balanced. This means that the total mass number (top number) and total atomic number (bottom number, representing charge) on the left side of the equation (reactants) must equal the total mass number and total atomic number on the right side (products and emitted particles). The mass number represents the sum of protons and neutrons in the nucleus, while the atomic number represents the number of protons. Balancing these numbers ensures conservation of mass and charge during the decay process.

Alpha (α) Decay

Alpha decay occurs when an unstable nucleus emits an alpha particle, which is identical to a helium nucleus ($^{4}_2$He). During alpha decay, the parent nucleus's mass number decreases by 4, and its atomic number decreases by 2. This changes the element. For example, if an element X undergoes alpha decay, it transforms into a new element Y with a mass number (A-4) and atomic number (Z-2). The general form is: $^{A}_Z$X → $^{A-4}_{Z-2}$Y + $^{4}_2$α.

Beta (β) Decay

Beta decay involves the emission of a beta particle, which is a high-energy electron ($^{0}_{-1}$e or $^{0}_{-1}$β). In this process, a neutron within the nucleus transforms into a proton, emitting an electron and an antineutrino. The mass number of the parent nucleus remains unchanged, but its atomic number increases by 1. This means the element changes to the next one in the periodic table. For example, if element X undergoes beta decay, it transforms into a new element Y with a mass number (A) and atomic number (Z+1). The general form is: $^{A}_Z$X → $^{A}_{Z+1}$Y + $^{0}_{-1}$β.

Gamma (γ) Emission

Gamma emission involves the release of gamma rays, which are high-energy electromagnetic radiation ($^{0}_0$γ). Gamma emission often occurs after alpha or beta decay when the daughter nucleus is left in an excited, unstable state. The nucleus releases the excess energy as gamma rays to reach a more stable ground state. Importantly, gamma emission does not change the mass number or the atomic number of the nucleus, so the element remains the same. It only removes excess energy from the nucleus. For example, $^{A}_Z$X* → $^{A}_Z$X + $^{0}_0$γ (where X* denotes an excited nucleus).

Understanding Half-Life

Half-life is the characteristic time period for a radioactive isotope. It is defined as the time taken for half of the unstable nuclei in a given sample to decay. Alternatively, it's the time required for the activity of a radioactive source to fall to half its initial value. This value is constant for a specific isotope and is not affected by external factors like temperature or pressure. For example, if an isotope has a half-life of 10 days, after 10 days, half of the original radioactive atoms will have decayed. After another 10 days (total of 20 days), half of the remaining half will decay, leaving one-quarter of the original atoms.

Radioactive Decay is Random

The decay of individual unstable nuclei is a spontaneous and unpredictable process. We cannot know precisely when a particular unstable nucleus will decay. This is known as the random nature of radioactive decay. While the decay of a single nucleus is random, in a large sample of radioactive material, the sheer number of nuclei means that statistical averages become reliable. This is why the half-life, despite individual randomness, is a consistent and measurable property for a radioactive substance. It represents the average behaviour of a vast number of atoms, not a prediction for a single one.

Calculating Remaining Activity/Nuclei

To determine the fraction of unstable nuclei remaining after a certain number of half-lives, or the remaining activity, you can repeatedly halve the initial quantity. After 1 half-life, 1/2 of the original amount remains. After 2 half-lives, (1/2) * (1/2) = 1/4 remains. After 3 half-lives, (1/2) * (1/2) * (1/2) = 1/8 remains. This pattern continues, where the fraction remaining is (1/2)^n, where 'n' is the number of half-lives passed. This principle is fundamental for calculations involving radioactive decay.

Unstable Nuclei and Radioactivity

Atomic nuclei can be unstable due to an imbalance in their proton and neutron composition. To become more stable, these nuclei undergo a process called radioactive decay. During this decay, they spontaneously emit energy and/or particles from their nucleus. This process leads to the formation of a different, more stable nucleus or a lower energy state of the same nucleus. Understanding these emissions is fundamental to studying radioactivity and its applications.

Types of Radioactive Emissions

There are three primary types of radiation emitted during radioactive decay: alpha particles, beta particles, and gamma rays. Alpha particles are positively charged, consisting of two protons and two neutrons (a helium nucleus). Beta particles are high-energy electrons with a negative charge. Gamma rays are uncharged, high-energy electromagnetic radiation. In some specific decay processes, neutrons may also be emitted from the unstable nucleus. Each type of emission has distinct characteristics regarding its mass, charge, and penetrating power.

Alpha Particle Emission

An alpha particle is effectively a helium-4 nucleus. When an unstable nucleus emits an alpha particle, its atomic number decreases by 2 (due to the loss of two protons), and its mass number decreases by 4 (due to the loss of two protons and two neutrons). Alpha particles are relatively heavy and slow-moving compared to other emissions. They have a strong ionising effect but are not very penetrating, being stopped by a sheet of paper or a few centimetres of air.

Beta Particle and Gamma Ray Emission

Beta decay occurs when a neutron in the nucleus transforms into a proton, emitting an electron (beta particle) and an antineutrino. This increases the atomic number by 1, while the mass number remains unchanged. Beta particles are lighter and faster than alpha particles, with moderate ionising power and penetrating power, stopped by a few millimetres of aluminium. Gamma rays are electromagnetic waves and carry no charge or mass. They accompany other decay processes and release excess energy from the nucleus. Gamma rays are highly penetrating, requiring thick lead or concrete to stop them, but have weak ionising power.