Magnets are objects with north/south dipoles that create a field around them. Although ferromagnetic substances can repel each other, paramagnetic substances are always attracted to a magnetic field. See [HL Chemistry#Physics properties of transition elements](/sch3uz/#physical-properties-of-transition-elements) for more details.
Similar to electric and gravitational fields, magnetic fields (also known as **B-fields**) are drawn by their effect on a north pole. Since magnetic poles always appear in equal magnitude pairs, all magnetic field lines for a magnet must form closed loops from north to south **outside** and south to north **inside** the magnet. Much like electric field lines, magnetic field lines never touch
Atoms in ferromagnetic materials are tiny magnets with **dipoles**. These dipoles act on neighbouring dipoles and can cause the whole object to align — this is known as an **electric domain**.
!!! note
Nickel, cobalt, or any alloy with nickel, cobalt, or iron can become magnetised this way.
**Unmagnetised** domains have dipoles pointing in random directions that are aligned when exposed to a magnetic field where they become **magnetised** domains. As such, bar magnets are always broken into smaller magnets, each with two poles — a monopole is impossible to create.
Moving electric charges produce magnetic fields. A circle filled with an "x" indicates that the current is moving away from the viewer in the third dimension while a dotted circle indicates it is moving toward the viewer.
These magnetic fields are centred on the conductor, are in a plane perpendicular to the conductor, and have decreasing magnetic field strength over distance.
The **right-hand rule** for straight-line conductors indicates that when the conductor would be grasped by the right hand, the thumb would point in the direction of current and the fingers pointing in the direction of the magnetic field.
A **selenoid** is a conductor coil in a tight helix. Current passed through a selenoid will generate a **uniform magnetic field** inside the coil with a pattern identical to that of a bar magnet outside it.
As only moving electric charges generate magnetic fields, stationary electric charges are **unaffected** by external magnetic fields. Moving charges are affected by Newton's third law of motion — equal and opposite forces are exerted on the charge and the magnet. As such, where $q$ is the charge of the particle and $\vec{v}\times \vec{B}$ is the **cross product** (vector multiplication) of the velocity of the particle and the magnetic field strength in Teslas:
$$\vec{F_m}=q\vec{v}\times \vec{B}$$
**Magnetic field strength** ($B$) represents the force acting per unit current in a conductor of unit length perpendicular to the field with the unit Tesla ($\pu{T}$)
The **magnetic force** is always plane **perpendicular** to both $\vec{v}$ and $\vec{B}$. Just the magnitude of the force can be found by using the angle between the two vectors ($\theta$):
$$|F_m|=qvB\sin\theta$$
Regardless of $\theta$, the force vector is always perpendicular to both $B$ and $v$,
The above equation can be rearranged to find **electromagnetic** force in terms of current and wire length in a **uniform magnetic field**:
The **right-hand-rule** can be used to determine the direction of force — the thumb points in the direction of current/velocity, the fingers point in the direction of the magnetic field, and the palm points in the direction of force. Alternatively, just three fingers can be used.
When two straight-line conductors with current flowing through them are brought together, they either mutually attract or repel. The ampere is defined based on the current required to flow through a scenario involving two parallel straight-line conductors.
Inside a **uniform magnetic field**, charges move in **uniform circular motion** at a constant velocity. If the particle did not enter the field at a perfect right angle, some of the velocity is used to change the path of the particle to be in a spiral — still perfectly circular, but additionally moving in the third dimension perpendicular to the circle.
- A **photon** is a particle that represents light.
- A **nucleon** is a subatomic particle in an atomic nucleus — that is, a proton or neutron.
- A **nuclide** is a nucleus with a specific number of protons and neutrons.
Please see [HL Chemistry#2.1 - Atoms](/sch3uz/#21-atoms) and [HL Chemistry 1#2.2 - Electrons in atoms](/sch3uz/#22-electrons-in-atoms) for more information.
An electron in an atom will only become excited if a photon of exactly the right amount of energy strikes it. That energy can be found using the formula:
$$\Delta E=hf$$
where $E$ is the energy of the photon at frequency $f$, and $h$ is Planck's constant ($\pu{6.63\times 10^{-34} Js}$ or $\pu{4.14\times10^{-16} eVs}$).
An electron that de-excites will emit a photon of that exact energy and thus frequency to return to its previous state.
### Binding energy
According to Einstein's theory of special relativity:
$$\Delta E=\Delta mc^2$$
**Neutrons** in the nucleus hold the protons together via **strong nuclear forces** that somewhat act like glue. An increase in neutrons increases the strong nuclear force. In smaller nuclei, $N=Z$, but in larger nuclei, $N>Z$ as more neutrons are required to keep the nucleus stable as the number of protons increases.
The mass of a stable nucleus is always less than the sum of the masses of the individual nucleons (the **mass defect**) as some of the mass is converted to energy during the formation of a nucleus. The energy used is known as the **binding energy** of a nucleus.
$$E_\pu{binding} = \pu{mass defect}\times c^2$$
As such, the binding energy of a nucleus is also the energy required to separate it completely into individual nucleons.
Atomic mass is measured relative to the mass of a carbon-12 atom, which is exactly 12 u (unified atomic mass units).
It is required to know the general shape of the curve, that $\pu{~8.8 MeV}$ is the maximum, and that the end boundaries are $0$ and $\pu{~7.5 MeV}$. It is also required to know the elements at each of those points (hydrogen-1, iron-56/nickel-62, and uranium-238).
Since a greater binding energy per nucleon is more energetically favourable, nuclei to the right of iron-56 fission (split) while those to the left fuse (combine) to release energy — changes that would increase binding energy per nucleon are likely to occur because of this.
### Radioactive decay
!!! definition
- An **alpha particle** is a helium-4 nucleus (2 protons, 2 neutrons).
- A **beta particle** is an electron.
- A **gamma ray** is a photon.
Radioactivity is the emission of **ionising** (will make ions) radiation due to changes of a nucleus. It is **random** and spontaneous — it is unaffected by external factors such as other nuclei decaying.
**Nuclear equations** are similar to chemical equations but show how nuclei change in a nuclear process by tracking the atomic and mass numbers. A nuclear equation is balanced so that the sum of the atomic and the sum of the mass numbers on both sides are equal.
$$A\to B+C$$
**Alpha decay** occurs when the strong nuclear force is unable to hold a large nucleus together and emits an alpha particle. The alpha particle is positive and can barely penetrate paper. The two particles move in opposite directions with momentums equal in magnitude.
**Beta-minus decay** ($\beta^-$) occurs when a neutron decays into a proton and releases a beta-minus particle (an electron and an electron antineutrino). It can penetrate up to 3 mm of aluminum. Where $\overline{v}_e$ is the antineutrino:
The bar over the electron antineutrino identifies it as an **antiparticle**.
The beta-minus particle can be written explicitly over the electron as $^0_{-1}\beta$.
In terms of the mother nucleus, the reaction results in the mass number staying the same while the atomic number increases by one.
**Beta-plus decay** ($\beta^+$) occurs when a proton decays into a neutron and releases a **positron** (an antielectron with a positive charge) and an electron neutrino ($v_e$)
$$\ce{^1_1p → ^1_0n + ^0_1e + ^0_0v_e}$$
The positron can be written as a beta-plus particle as $^0_1\beta$.
In terms of the mother nucleus, the reaction results in the mass number staying the same while the atomic number decreases by one.
**Gamma decay** occurs when an excited nucleus transfers its energy to a high-energy photon with frequencies in the gamma region of the electromagnetic spectrum. There is no change in mass nor atomic number. A nuclide with an asterisk $*$ indicates it as excited. This emits *ionising radiation* which is not good for living beings.
As radiation cannot be seen, it must be detected experimentally.
A **Geiger counter** utilises a gas-filled tube with a wire in the centre at high voltage. When a charged particle passes through, gas is ionised which cascade onto the wire to produce a pulse.
A **cloud chamber** contains vapour that turns into liquid droplets when ionising particles pass though, resulting in visible lines showing the path of the particles. A magnetic field can spiral the particle in a certain direction which allows for its charge to be identified.
### Half-life
The **half-life** of an element is the time required for half of the nuclides in a sample to decay — it is always the same no matter the number of initial nuclides.
As such, this means that the number of parent nuclei decreases by 50% of its current value each half-life.
**Radioactive dating** analyses the ratio between carbon-14 and carbon-12 to determine the age of plant nmatter. As the ratio of C-14 and C-12 in the atmosphere has been relatively comstant, living plants maintain that balance by constantly exchanging carbon. Dead plants' carbon-14 slowly decay at a known rate, so the ratio can be used to determine the time since the plant died.