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The Nucleus and Radioactivity

As soon as physicists discovered that matter consists of atoms, and that these atoms are made up of smaller particles, the electron (discovered in 1897), the proton (discovered in 1917), and the neutron (discovered in 1932), they have been trying to split the atom to discover its properties. One of these 'properties' was the fission of large atoms to release enormous amounts of energy, which could be used for generating energy, but also unfortunately for weapons of mass destruction.

Alpha, Beta, and Gamma Radiation

When the atomic nucleus was first split, three types of radiation were observed being emitted. It was not known what they were, so they were called 'A', 'B', and 'C' radiations, but scientists being scientists they used Greek letters: α (alpha), β (beta), and γ (gamma), just to jazz it up a little.

AlphaBetaGamma
Mass$6.64 × 10^{-27}$ kg$9.1 × 10^{-31}$ kg0
Charge+2e-e0
ParticleHe nucleuselectron (fast)photon
Shielding requiredA few cm of air1-2 cm of paper, thin metalThick lead
Ions per mm of air for 2MeV$10^4$$10^2$1

Ionisation: these radiations strip electrons off molecules in the air, or any media they pass through, so are referred to as ionising radiation. Although short-lived, alpha particles are much more ionising than beta particles, which in turn are much more ionising than gamma radiation.

Alpha Radiation

Alpha radiation is a stream of particles. These particles consist of two protons and two neutrons - in effect the nucleus of a helium atom. Alpha particles therefore have a charge of +2e, and are detectable because their trajectory can be curved by a magnetic field.

Alpha particles ionise the material they passes through, and interact with it. After a short distance, called the range, which depends on its energy, an alpha particle will be absorbed by the medium (e.g. air).

Examples of alpha radiation equations:

Uranium-Thorium decay: $ {\table {238};{92}}$U $ → {\table {238};{92}}$Th $ + {\table {4};{2}}$α

Radium-Radon decay: $ {\table {224};{88}}$Ra $ → {\table {220};{86}}$Rn $ + {\table {4};{2}}$α

Polonium-Lead decay: $ {\table {212};{84}}$Po $ → {\table {208};{82}}$Pb $ + {\table {4};{2}}$α

Beta radiation

Beta (β) radiation consists of a stream of fast electrons (charge -e). Thomson's e/m experiment induces behaviour which is dependent on the ratio of charge to mass. This was used to identify the -e charge and very low mass of the beta particles. However, since the electrons were travelling very fast, near the speed of light, their behaviour was affected by special relativity, whereby the mass increases at very high speeds. Beta particles were therefore an early test for special relativity.

Examples of beta radiation equations:

Thorium-Protactinium β-decay: $ {\table {234};{90}}$Th $ → {\table {234};{91}}$Pa $ + {\table {0};{-1}}$e + ${\table {0};{0}}\ovν_e$

where ${\table {0};{0}}\ovν_e$ is the electron antineutrino.

This may also be written as: $ {\table {234};{90}}$Th $ →↖{β-} {\table {234};{91}}$Pa $ + {\table {0};{-1}}$e + ${\table {0};{0}}\ovν_e$

Other examples of β-decay:

Lead-Bismuth β-decay: $ {\table {214};{82}}$Pb $ →↖{β-} {\table {214};{83}}$Bi $ + {\table {0};{0}}\ovν_e$

Carbon-Nitrogen β-decay: $ {\table {14};{6}}$C $ →↖{β-} {\table {14};{7}}$N $ + {\table {0};{0}}\ovν_e$

Gamma radiation

Studying the refraction patterns of the third, chargeless radiation revealed it to be not a particle with mass, but a massless photon of electromagnetic radiation, with a wavelength smaller than x-rays, putting it at the top of the EMR spectrum (<$10^{-12}$). Short wavelength radiation is high-frequency, and very energetic.

Gamma rays will ionise on average one air molecule per millimetre of air.

Example of gamma photon radiation:

Uranium-238: $ {\table {238};{92}}$U* $ → {\table {238};{92}}$U $ + {\table {0};{0}}$γ

where the asterisk (*) indicates the uranium atom is in an excited state (energy level above the atom's ground state).

Nuclei can have only precise energy states (quantum levels). Photons are emitted at precise energies equal to the difference in energy states before and after the photon is emitted. Photons are emitted according to:

$$λ = {hc}/{ΔE}$$

where λ is the frequency of the photon (colour in the case of visible light), $h$ is Planck's constant ($6.63 × 10^{-34}$ Js), and $c$ is the speed of light in a vacuum ($3.0 × 10^{8}$ $m/s$).

The typical energies involved in quantum nuclei energy states are a few MeV (1 eV = $1.602 × 10^{-19}$ J).

1.0 MeV radiation therefore has a wavelength of:

$λ = {hc}/{ΔE} = {(6.63 × 10^{-34}) Js × (3.0 × 10^{8}) ms^{-1}}/{1 × 10^{6} eV} = (2.0 × 10^{-25} Jm)/(1.602 × 10^{-13} J) = 1.2 × 10^{-12} m$

Law of Radioactive Decay

The law of radioactive decay states that the rate of decay of nuclei is proportional to the number of atoms present which have not yet decayed.

Due to the quantum nature of nuclei, it is not possible to be precise about any particular nucleus. We can only describe the probability of decay events.

The half-life of an isotope is the time it takes a population of atoms of the isotope to decay till there remain only half the number of the original population.

For any mass of a radioactive substance, there is an exponentially decreasing number of decay events through time. After one half-life, half of the isotopes have decayed. After a second half-life has elapsed, half of the remaining isotopes (i.e. one-quarter of the original amount) will have decayed (leaving only 1/4). After a third half-life, one-eighth remain. Four half-lives: $1/{16}$, and so on.

The number of decays per second is called the activity. The unit of activity is the becquerel (Bq) (after the French physicist Henri Becquerel, 1852 - 1908), which is equal to one decay per second.

Nuclear Reactions

Binding Energy

The binding energy is the energy needed to hold a nucleus of an atom together.

Unified Mass Unit u

The S.I. base unit for mass is the kilogram. The masses of the particles that make up an atomic nucleus, the proton and the neutron, are so close in mass a unit has been invented just for them: the unified mass unit (u).

Avogadro's constant is based on the mass of carbon-12, the isotope of carbon with 6 protons and 6 neutrons. The unified mass unit, symbol u, is also based on this isotope, and is equal to $1/{12}$ the mass of the carbon-12 isotope.

Mass (kg)Mass (u)
Unified mass unit$1.6605402 x 10^{-27}$1
Neutron$1.6749286 x 10^{-27}$1.008665
Proton$1.6726231 x 10^{-27}$1.007276
Electron$9.1093897 x 10^{-31}$0.0005486
Mass Defect

The energy that is needed to hold the nucleons of an atom together is the binding energy. The binding energy is obtained by the conversion of some of the mass of the nucleons, according to $E = mc^2$, to energy. This leaves a difference in mass between the mass of the individual nucleons, and the mass of the nucleus. The mass of the nucleus is always less than the mass of the individual protons and neutrons measured outside the nucleus, and this difference is known as the mass defect. The mass defect is (mass of nucleons) - (mass of nucleus):

$$δ = Zm_p + (A - Z)m_n - M_{nuc}$$

where δ is the mass defect, $Z$ the atomic number (no. of protons), $m_p$ the mass of a proton, $A$ the atomic mass (∴ $A-Z$ is the number of neutrons), $m_n$ the mass of a neutron, and $M_{nuc}$ is the mass of the nucleus.

For example, the atomic weight of uranium-235 is $235.0439299$ u. It has 92 protons and 143 neutrons. The mass of the nucleus is the atomic weight minus the mass of the electrons (equal in number to the protons):

Mass of uranium-235 nucleus = atomic weight - mass of the electrons = $235.0439299 - (92 × 0.0005486) = 234.9934587$ u

The mass of the nucleons is: (no. neutrons x mass of one neutron) + (no. protons x mass of one proton) $= (143 × 1.008665) + (92 × 1.007276) = 236.908487$ u

The mass defect, δ = mass of nucleus - mass of nucleons = 236.908487 u - 234.9934587 u = 1.9150283 u

Using $E = mc^2$, the binding energy of one unified mass unit is 931.5 MeV. Therefore:

$E_b = 1.9150283u × 931.5$ MeV $ = 1783.8$ MeV

Nucleon binding energies

The binding energy, $E = δc^2$, of the nucleus is equal to the work done to separate the nucleons of a nucleus. The higher the binding energy, the more stable a nucleus is.

Content © Andrew Bone. All rights reserved. Created : March 1, 2014 Last updated :December 23, 2015

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