---
title: Introduction
allDay: false
startTime: 18:00
endTime: 21:00
date: 2024-08-27
completed: null
---
# Parts and things related to atoms
Four main components
1. **Electron**
	1. Basically massless. 
	2. Don't have a huge effect on the nuclear physics.
2. **Proton**
	1. Do have mass! 
	2. Determine what the element is.
3. **Neutron**
	1. Are the fuel. Hit things fast
	2. Don't change element by number.
	3. 
4. **Photon**
	1. Don't really interact with matter
	2. Can actually be a safety concern. Can harm people.
5. Bonus! **Neutrino**
	1. Basically no mass.
	2. Balance out the energy equations.
	3. Light :)

The nucleus is really, really small.
For $^4 He$ , $V_\text{nucleus} / V_\text{atom} = 2.6\times 10^-12$ 

# Atom Identification
## $^A_Z X$ 
* A is the atomic mass
* Z is the atomic number
* X is the element symbol
Some examples:
$^{235}_{92} U$ $^4_2 He$ $^1_1 H$ 

**Nuclide** - A type of atom characterized by the number of protons and neutrons in the nucleus of every atom of this type
**Isotopes** - Atoms with the same number of protons but containing different numbers of neutrons.
**Isotopic Abundance** - The percentage of an element that is a certain isotope. Sometimes abbreviated (a/o)
**Atomic Weight** - The average weight of all isotopes weighted by their prevalence.

*Atomic Weight of $^A Z$   = $12 \frac{m\left(^A Z\right)}{m\left(^{12}C\right)}$ . 
Atomic mass of Z is in the slides

**Molecular weight** is the total mass of a molecule relative to the mass of a neutral $^{12}C$. 
# Mass and Energy Equivalence
Einstein famously showed that $E = m c^2$
Electron volts are a unit
![[Pasted image 20240827190612.png]]

# Forces in the nucleus
1. Nuclear (Strong) force (Attractive)
2. Coulomb force (repulsive)
In a stable atom, these are balanced forces.

Some ways atoms are unstable:
1. Proton rich
	1. Way too much Coulomb force
	2. They will split!
2. Neutron rich
	1. Not enough Coulomb force
	2. Will want to shift around, and will shed neutrons

If the ratio of neutrons to protons is between 1-2, the atom is stable.

# Nuclear Decay
Nature will always break apart unstable atoms:
1. Convert neutrons into protons (or v.v.)
2. Split into two nuclei
3. Eject a particle

1 Normally happens for lower atomic number atoms. As nuclei get bigger, the strong force is less powerful and the ejection can actually happen.

## Decay Modes
1. Emit a nucleon
	1. proton emission (rare)
	2. double proton (rarer)
	3. neutron emission (rare)
	4. alpha decay (common!)
	5. cluster decay(rare)

### Alpha Decay
4 amu mass, charge +2. Helium nucleus. Most common decay mode for nuclei with Z>90.

### Breaking Apart (Spontaneous fission)
Much less common than alpha decay.
Occurs for nuclei 2Z/A >45

### Changing Nucleon Type
Most common for smaller atoms
Two basic modes: both are beta decay (+/-)
	Negative turns a neutron into a proton, emit an electron
	Positive turns a proton into a neutron, emit a positiron
		This mf gets obliterated pretty damn fast. That atom then becomes an ion. Emits a couple of photons.
	electron capture! Proton will absorb an inner cloud electron.
Neutrinos also get ejected

![[Pasted image 20240827193439.png]]

## Chart of the Nuclides
The chart of the nuclides is how we understand chains of decay, and what will turn in to what. 
![[Pasted image 20240827195025.png]]
[A potentially useful interactive website](https://people.physics.anu.edu.au/~ecs103/chart/)

# Radiation
Any process that releases energy is referred to as radioactive decay. 
**Radionuclide** - an unstable nuclide that is going to decay.

Types of radiation
1. Electromagnetic - Energy transmitted as electromagnetic waves
	1. radio, microwave, infrared, etc
	2. Characterized by its frequency
	3. wave-particle business
	4. Photons!
	5. Ionizing at the gamma / x ray range. 
		1. gamma $\gamma$ rays are super high energy
		2. They happen when atoms rearrange themselves. Excess energy is emitted as a gamma ray.
2. Ionizing Radiation - Enough energy to remove one or more electrons from an atom

# Doing Math
## Nuclear Decay
Decay is a random process.
**Decay constant:**
$$\lambda = \frac{\text{decay}}{\text{nucleus-second}}$$

Activity is the amount of decays per second
$N$ is the number of nuclei present. these are functions of time.
**Activity:**
$$ A(t) = \lambda N(t) $$
$$N(t) = N(0) e^{-\lambda t}$$
Half life is a derivative of activity:

$$ t_{1/2} = \frac{0.693}{\lambda}$$
We can also talk about decay in terms of time instead of instances of decay
**Mean Lifetime:**
$$ \tau = \frac{1}{\lambda}$$
