140 lines
4.5 KiB
Markdown
140 lines
4.5 KiB
Markdown
---
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title: Introduction
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allDay: false
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startTime: 18:00
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endTime: 21:00
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date: 2024-08-27
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completed: null
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---
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# Parts and things related to atoms
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Four main components
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1. **Electron**
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1. Basically massless.
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2. Don't have a huge effect on the nuclear physics.
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2. **Proton**
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1. Do have mass!
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2. Determine what the element is.
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3. **Neutron**
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1. Are the fuel. Hit things fast
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2. Don't change element by number.
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3.
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4. **Photon**
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1. Don't really interact with matter
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2. Can actually be a safety concern. Can harm people.
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5. Bonus! **Neutrino**
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1. Basically no mass.
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2. Balance out the energy equations.
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3. Light :)
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The nucleus is really, really small.
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For $^4 He$ , $V_\text{nucleus} / V_\text{atom} = 2.6\times 10^-12$
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# Atom Identification
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## $^A_Z X$
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* A is the atomic mass
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* Z is the atomic number
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* X is the element symbol
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Some examples:
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$^{235}_{92} U$ $^4_2 He$ $^1_1 H$
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**Nuclide** - A type of atom characterized by the number of protons and neutrons in the nucleus of every atom of this type
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**Isotopes** - Atoms with the same number of protons but containing different numbers of neutrons.
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**Isotopic Abundance** - The percentage of an element that is a certain isotope. Sometimes abbreviated (a/o)
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**Atomic Weight** - The average weight of all isotopes weighted by their prevalence.
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*Atomic Weight of $^A Z$ = $12 \frac{m\left(^A Z\right)}{m\left(^{12}C\right)}$ .
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Atomic mass of Z is in the slides
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**Molecular weight** is the total mass of a molecule relative to the mass of a neutral $^{12}C$.
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# Mass and Energy Equivalence
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Einstein famously showed that $E = m c^2$
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Electron volts are a unit
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![[Pasted image 20240827190612.png]]
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# Forces in the nucleus
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1. Nuclear (Strong) force (Attractive)
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2. Coulomb force (repulsive)
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In a stable atom, these are balanced forces.
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Some ways atoms are unstable:
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1. Proton rich
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1. Way too much Coulomb force
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2. They will split!
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2. Neutron rich
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1. Not enough Coulomb force
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2. Will want to shift around, and will shed neutrons
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If the ratio of neutrons to protons is between 1-2, the atom is stable.
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# Nuclear Decay
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Nature will always break apart unstable atoms:
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1. Convert neutrons into protons (or v.v.)
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2. Split into two nuclei
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3. Eject a particle
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1 Normally happens for lower atomic number atoms. As nuclei get bigger, the strong force is less powerful and the ejection can actually happen.
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## Decay Modes
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1. Emit a nucleon
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1. proton emission (rare)
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2. double proton (rarer)
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3. neutron emission (rare)
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4. alpha decay (common!)
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5. cluster decay(rare)
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### Alpha Decay
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4 amu mass, charge +2. Helium nucleus. Most common decay mode for nuclei with Z>90.
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### Breaking Apart (Spontaneous fission)
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Much less common than alpha decay.
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Occurs for nuclei 2Z/A >45
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### Changing Nucleon Type
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Most common for smaller atoms
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Two basic modes: both are beta decay (+/-)
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Negative turns a neutron into a proton, emit an electron
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Positive turns a proton into a neutron, emit a positiron
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This mf gets obliterated pretty damn fast. That atom then becomes an ion. Emits a couple of photons.
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electron capture! Proton will absorb an inner cloud electron.
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Neutrinos also get ejected
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![[Pasted image 20240827193439.png]]
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## Chart of the Nuclides
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The chart of the nuclides is how we understand chains of decay, and what will turn in to what.
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![[Pasted image 20240827195025.png]]
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[A potentially useful interactive website](https://people.physics.anu.edu.au/~ecs103/chart/)
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# Radiation
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Any process that releases energy is referred to as radioactive decay.
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**Radionuclide** - an unstable nuclide that is going to decay.
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Types of radiation
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1. Electromagnetic - Energy transmitted as electromagnetic waves
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1. radio, microwave, infrared, etc
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2. Characterized by its frequency
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3. wave-particle business
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4. Photons!
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5. Ionizing at the gamma / x ray range.
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1. gamma $\gamma$ rays are super high energy
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2. They happen when atoms rearrange themselves. Excess energy is emitted as a gamma ray.
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2. Ionizing Radiation - Enough energy to remove one or more electrons from an atom
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# Doing Math
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## Nuclear Decay
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Decay is a random process.
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**Decay constant:**
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$$\lambda = \frac{\text{decay}}{\text{nucleus-second}}$$
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Activity is the amount of decays per second
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$N$ is the number of nuclei present. these are functions of time.
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**Activity:**
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$$ A(t) = \lambda N(t) $$
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$$N(t) = N(0) e^{-\lambda t}$$
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Half life is a derivative of activity:
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$$ t_{1/2} = \frac{0.693}{\lambda}$$
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We can also talk about decay in terms of time instead of instances of decay
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**Mean Lifetime:**
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$$ \tau = \frac{1}{\lambda}$$
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