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Nuclear Radiations
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The nucleus
A nucleus consists of protons and neutrons; these are known as nucleons. Each nucleus is characterized by two numbers: A , the atomic mass number (the total number of nucleons); and Z , the atomic number (the number of protons). The number of neutrons is N , so A = N + Z. Any nucleus can be written in a form like this:
The X stands for the chemical symbol. On the right is a particular isotope of aluminum, aluminum-27. Isotopes of an element have the same Z , but different number of neutrons.
A 27
Z X^13 Al
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How big is a nucleus?
How big is a nucleus?
We know that atoms are a few angstroms, but most of the atom is empty space. The nucleus is much smaller than the atom, and is typically a few femtometers. 1 fm = 1 x 10 -15^ m.
The nucleus can be thought of as a bunch of balls (the protons and neutrons) packed into a sphere, with the radius of the sphere being approximately:
r = 1.2 x 10 -15^ A1/3^ r
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The atomic mass unit
The mass of a tiny object like a neutron or an atom is often stated in terms of the atomic mass unit (u). The atomic mass unit is defined in terms of the mass of:
- an electron
- a proton
- a neutron
- a hydrogen atom
- a helium 4 atom
- a carbon 12 atom
- a carbon 14 atom
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The atomic mass unit
1 u = (Mass of 12 C atom)/
= 1.660540 × 10 -27^ kg
= 931.5 MeV/c 2
931.5 MeV/c 2 =1.66054x10 -27kgx(3x10 8 m/s) 2 )/(1.6x10-19eVx10 6 )
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A table of masses
One atomic mass unit (u) is defined as 1/12th^ the mass of a carbon 12 atom.
Particle Mass (kg) Mass (u) Mass (MeV/c^2 ) 1 atomic mass unit
1.660540 × 10 -27^ 1.000 931.
neutron 1.674929 × 10 -27^ 1.008664 939. proton 1.672623 × 10 -27^ 1.007276 938.
electron 9.109390 × 10 -31^ 0.00054858 0.
A carbon 12 atom is made up of 6 e-^ , 6 p and 6 n. Let’s check how the sum of 6m (^) n + 6m (^) p + 6m (^) e compares with 12u.
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The mass defect
Using the mass data, we can find the sum of masses for 6 neutrons, 6 protons, and 6 electrons:
six neutrons: 6 1.008664 u 6.051984 u
six protons: 6 1.007276 u 6.043656 u
six electrons: 6 0.00054858 u 0.00329148 u
Sum = 12.098931 u
On the other hand, when these particles are combined into a carbon-12 atom, the atom has a mass of precisely 12.000000 u. The missing 0.098931 u worth of mass is called the mass defect. 8
The most famous equation in physics
The missing mass is the binding energy of the atom (almost all of that energy is in the nucleus).
By expressing the mass defect in MeV/c 2 (using 1 u = 931.5 MeV/c 2 ), one gets a direct reading of the binding energy in MeV. For example with carbon-12, the mass defect of 0.098931 u converts to 92. MeV/c 2. This corresponds to a binding energy of E = (92.15 MeV/c^2 )(c 2 ) = 92.15 MeV.
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E mc
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Nuclear processes
In a typical nucleus, the binding energy is measured in MeV, considerably larger than the few eV associated with the binding energy of electrons in an atom. Nuclear processes (such as nuclear reactions or decays) involve changes in the nuclear binding energy. This is why nuclear reactions can give much more energy than chemical reactions, where only changes in electron binding energy are involved.
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Holding the nucleus together
A typical nucleus has a number of protons and neutrons packed together in a small space. In PY105 and 106, we had discussed quite a few different kinds of forces. Which of these forces is primarily responsible for holding the nucleus together?
- gravity
- tension
- electrostatic
- magnetic
- none of the above
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Holding the nucleus together
The nucleus is tiny, so the protons are all very close together. The gravitational force attracting them to each other is much smaller than the electric force repelling them, so there must be another force keeping them together. This other force is known as the strong nuclear force.
The strong nuclear force is a very strong attractive force for protons and neutrons separated by a few femtometers, but it is basically negligible for larger distances.
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The strong force
The tug of war between the attractive strong force and the repulsive electrostatic force between protons has implications for the stability of a nucleus. Atoms with very low atomic numbers have about the same number of neutrons (N) and protons (Z). This is because the nucleus gains stability by having N = Z. As Z gets larger, there is more electrostatic repulsion so large nuclei need more neutrons (which increases the strong force without adding electrostatic repulsion) than protons for stability. Eventually, a point is reached beyond which there are no stable nuclei. The bismuth nucleus with 83 protons and 126 neutrons is the largest stable nucleus. Unstable nuclei undergo radioactive decay to transform into more stable daughter nuclei.
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Z
N
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Alpha decay - an example
An example of alpha decay meeting all these requirements involves Radium 226:
(^22688) Ra (^22286) Rn 24 He
The product, Radon 222 is a gas in soil and can leak into the basement of homes through cracks in the foundation. Currently, there is a national concern about the health hazards of radon.
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Alpha decay – another example
The left side of the equation has more mass (or less mass defect), by 0.004587 u. Where did the extra mass go?
The mass difference was converted to 0.004587 u × 931.5 MeV/u = 4.273 MeV of energy. This shows up in the kinetic energy of the two atoms after the reaction.
Reactions occur spontaneously when the total mass afterwards is less than the total mass before.
238 234 4
92 U^ ^90 Th 2 He
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Important: General requirements for a
permissible radioactive decay
(1) The total mass of the daughter nuclides must be smaller than that of the parents. This is effectively saying that the daughter nuclides are on average more stable than the parent nuclides
(2) The sum of the atomic numbers and mass numbers of all the parent nuclides/particles and daughter nuclides/particles before and after the decay must agree. In checking if this requirement is met, take for neutrons ( 10 n), A = 1 and Z = 0; for protons ( 11 p), A = 1 and Z = 1; and for electrons ( (^0) -1 e), A = 0 and Z = -1.
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Beta decays
In these decays, either a -minus particle (which is an electron) or a -plus particle (which is a positron or a positively-charged particle that is the anti- matter equivalent of the electron) is emitted.
In terms of safety, beta particles are more penetrating than alpha particles, but less than gamma particles.
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Beta-minus (β-) decay
1 1 0 -
0 n^ ^1 p^ ^ -1 e^ νe
e
A Z
A
Z X ^ Y e ^
0 Generally, 1 1
The particle labeled e is an antineutrino. The “e” subscript and the over bar denote that it is an electron antineutrino. Notice that it has A=0 (negligible mass) and Z=0 (no charge), and you don’t need to consider it in balancing the total A and Z in the equation. The existence of the neutrino was proposed by Wolfgang Pauli in 1930 to explain what seemed like violations of the laws of conservation of energy and conservation of momentum in the beta decay process.
For nuclides with N/Z being too large
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Z
N
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Beta-minus decay – an example
An example of beta decay is:
Use the data from the appendix: The atomic mass of Th^234 (thorium) is 234.043596 u The atomic mass of Pa^234 (protactinium) is 234.043302 u We don't have to add the mass of the electron because the mass for Pa 234 includes 91 electrons, which is how many we have on the right side. It's already built into the mass for Pa^234. The mass of the anti-neutrino is non-zero, but negligible.
234 234 0 -
90 Th ^91 Pa^ ^ -1 e^ νe
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Beta-plus (β+) decay
In beta-plus decay, a proton turns into a neutron, a positron, and an electron neutrino. In general, we get:
1 1 0 +
1 p^ ^0 n^ ^ +1 e^ νe
A A 0 +
Z X^ ^ Z-1Y ^ +1 e^ νe
For nuclides with N/Z being too small
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Z
N
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Gamma decay
The third class of radioactive decay is gamma decay, in which the nucleus changes from a higher- level energy nuclear state to a lower level energy state. The nucleus has energy levels, similar to electron levels.
When an electron changes levels, the energy involved is usually a few eV, so a visible or ultraviolet photon is emitted. In the nucleus, energy differences between levels are much larger, typically a few hundred keV, so the photon emitted is a gamma ray. 30
Gamma decay
Gamma rays are very penetrating; they can be most efficiently absorbed by a relatively thick layer of high-density material such as lead. A gamma decay is written in the following way:
The asterisk indicates that the nucleus is in an excited state. Note that this is the only kind of radioactive decay in which the atom does not become another element.
A A
Z X^ ZX^
For nuclides with an excited nucleon
