Nuclear Physics

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Atoms

• Central part of an atom is the nucleus
• Consists of:
  • Neutrons
    • No charge: 0
    • Relative Atomic Mass: 1
  • Protons
    • Positive Charge +
    • Relative Atomic Mass: 1
• Collectively called nucleons
• Almost identical in mass and size
• Most of an atom is empty space that is only occupied by electrons
• Any change in the amount of protons changes the element 
• Electrons
  • Negative Charge: -
  • Relative Atomic Mass: 1/1836
  • Orbit nucleus at high speeds ${}_Z^{A}X$ A: Mass number
• No. of Neutrons + No. of Protons Z: Atomic number 
• Number of protons in the atom

Isotopes

• All atoms of a particular element have the same amount of protons
• However, they may have a different amount of neutrons
• Isotopes are chemically identical to each other
• They react and bond with other atoms in the exact same
• Number of neutrons does not affect in which an atom interacts with other atoms
• It is the electrons that determine this
• It affects the physical properties
• More neutrons in the atom means that the atom will be more dense
• When referring to a particular nucleus, we refer to it as a “nuclide”
• In this case, we ignore the presence of the electrons

Radioisotopes

• Most of the atoms that make up the world are stable
• Their nuclei have not changed, and will not change independently
• However there are also naturally occurring isotopes that are unstable
• An unstable nucleus may spontaneously lose energy by emitting a particle
• They change into a different element or isotope
• Unstable atoms are radioactive
• An individual radioactive isotope is called a radioisotope
• Nearly all elements found in the Earth’s crust have naturally occurring isotopes
• Over 2000 known radioisotopes, most of which are artificially produced

Alpha, Beta, and Gamma Radiation

• Around 100 years ago as of 2022, Ernest Rutherford and Paul Villard discovered that there were 3 different types of emission from radioactive substances
• They called these Alpha, Beta and Gamma Radiation
• Further experiments showed that the alpha and beta emissions were actually particles expelled from the nucleus
• Gamma radiation was found to be high-energy electromagnetic radiation, also emanating from the nucleus

Alpha Decay: $\alpha$

• When a heavy nucleus undergoes radioactive decay, it may eject an alpha particle
• Alpha particle: positively charged chunk of matter
• Consists of 2 protons and 2 neutrons
• Ejected from nucleus of a radioactive atom
• Ionising ability: ability to create ions
  • High ionising ability, as it has a high positive charge, and can displace electrons from other atoms
  • Since it is positively charged, it collides with a lot of other atoms and loses energy, dislodging electrons from those atoms
• An alpha particle is identical to a helium nucleus 
• Very massive
• Heavily charged
• Usually from heavy elements ${}_2^{4}H{e}^{2+}$ ${}_2^4{\alpha }^{2+}$ Example Uranium-238 is radioactive and may decay by emitting an alpha particle from its nucleus. This can be represented in a nuclear equation where the changes occurring in the nuclei can be seen. Electrons are not considered in these equations, only nucleons. The equation for the alpha decay of uranium-238 is: ${}_{92}^{238}U-{>}_{90}^{234}Th{+}_2^{4}H{e}^{2+}+energy$ In the decay process, the parent nucleus 238-92-U has spontaneously emitted an alpha particle (⍺) and has changed into a completely different element, 234-90-Th. Thorium-234 is called the daughter nucleus. The energy released is mostly kinetic energy carried by the fast-moving alpha particle. When an atom changes into a different element, it is said to have undergone a nuclear transmutation. In nuclear transmutations, electric charge is conserved—seen as a conservation of atomic number In the example, 90+2 = 92. The number of nucleons  is also conserved; 234+4 = 238.

Beta Decay

• Beta particles are electrons

• Originated from nucleus of a radioactive atom 

• Not from electron cloud

• Can be written as: ${}_{-1}^0{e}^{-}$ ${}_{-1}^0{\beta }^{-}$

• The atomic number of -1 indicates that it has a single negative charge

• Mass number of 0 indicates its mass is far less than a proton or neutron

• Beta decay occurs in nuclei where there is an imbalance of neutrons to protons

• Typically, if a light nucleus has too many neutrons to be stable, a neutron will spontaneously change into a proton

• Ionising ability is medium

  • Since it is negatively charged, it is repelled by the electron cloud of other atoms
  • Experiences a large number of collisions, but expends less energy from them
  • Therefore less ionising

• Electron and a uncharged massless particle called an antineutrino are ejected to restore the nucleus to a more stable state

• Antineutrino is symbolised as $\overline{V}$

Example Isotopes of carbon: C-12-6, C-13-6 and C-14-6. Carbon-12 and 13 are both stable, but carbon 14 is unstable. It has more neutrons, and therefore undergoes a beta decay to be stable. In the process, one of the neutrons changes into a proton. As a result, the proton number increases to 7, and so the product is not carbon. Nitrogen-14 is formed. The nuclear equation for this decay is: ${}_6^{14}C->{}_6^{14}N+{}_{-1}^{0}e+\overline{V}+energy$The transformation taking place in the nucleus is: ${}_0^{1}n-{>}_0^{1}p{+}_{-1}^{0}e+\overline{V}$

• n: neutrons
• p: protons
• e: beta particle Once again, notice how in all these equations, the atomic and mass numbers are conserved. The antineutrino has no charge and has so little mass that both its atomic and mass numbers are 0

Beta Decay (Positrons)

• A different form of beta decay occurs in atoms that have too many protons
• A proton may change into a neutron, emitting a neutrino and a positively-charged beta particle (β+). This is known as a β+ (beta-positive) decay and the positively charged beta particle is called a positron
• Positrons have the same properties as electrons, but their electrical charge is positive rather than negative. Positrons are an example of antimatter.

Example The radioactive decay of unstable nitrogen-12. There are 7 protons and 5 neutrons in the nucleus, and a proton may change into a neutron, emitting a neutrino and a positively-charged beta particle (β+). This is known as a β+ (beta-positive) decay and the positively charged beta particle is called a positron. The equation is: ${}_6^{14}N-{>}_6^{14}C+{}_{+1}^{0}e+\overline{V}+energy$

Gamma Decay

• Generally, after a radioisotope has emitted an alpha/beta particle, the daughter nucleus holds an excess of energy
• The protons and neutrons in the daughter nucleus then rearrange slightly and offload this excess energy by releasing gamma radiation (high-frequency electromagnetic radiation)
• Ionising ability is low
  • Interact with matter infrequently when they collide directly with the nucleus or an electron
  • Low density of the atom makes this infrequent, therefore it cannot dislodge electrons as much as beta particles
  • Low ionisation ability
• Gamma rays—like all light—have no mass and are uncharged
• However, it contains a lot of energy
• Symbol is: ${}_0^0\gamma$
• Being a form of light, gamma rays travel at the speed of light
• Gamma rays are a form of electromagnetic radiation/waves, and have the shortest wavelength
• They are photons

Example: A common example of a gamma ray emitter is iodine-131. Iodine-131 decays by beta and gamma radiation to form xenon-131. The equation for this is: ${}_{53}^{131}I->{}_{54}^{131}Xe{+}_{-1}^{0}e{+}_0^0\gamma$ These equations can also be written with $\alpha ,\beta$ or $\gamma$ written over the reaction arrow

Type of Radiation	Alpha	Beta	Gamma
Symbol	${}_2^{4}He$ or ${}_2^4\alpha$	${}_{-1}^0{\beta }^{-}$ or ${}_{-1}^0{e}^{-}$	${}_0^0\gamma$
Mass (amu)	4	$\frac{1}{1836}$	0
Charge	2+	-	0
Speed	slow	fast	very fast (speed of light = $3\times 10^{8}m{s}^{-}1$)
Ionising ability	high	medium	low
Penetrating ability	low	medium	high
Stopped by:	paper	aluminium	lead
Remember:	Atomic number decreases by 2, atomic mass decreases by 4	Atomic number increases by 1, atomic mass is unchanged	Atomic number and atomic mass are unchanged

Electromagnetic Waves

• Form of energy that emits in waves
• Transfers energy without transferring matter
• Can pass through vacuums
• Shorter the wavelength, higher the frequency
• This energy is mainly expressed as light, but can be expressed as heat or electricity
• Radiation can be emitted in the form of electromagnetic waves (gamma rays)

Half Life

• When a radioactive element decays, the number of radioactive nuclei decreases with time
• The time it takes for the number of radioactive nuclei to decrease to half its original amount is called its half-life