Nucleus & Nuclear Radiation
AGEN-689Advances in Food Engineering
Nuclear Structure
The nucleus of an atom of atomic number Z and mass number A consist of Z protons and N = A-Z neutronsA gives the total # of nucleons (protons and neutrons)Nuclide: a species of atom characterized by its nuclear constitution (its value of Z and A (or N))
•Unstable atoms are radioactive: their nuclei change or decay by spitting out radiation, in the form of particles or electromagnetic waves.
IsotopesAtoms of the same element can have different numbers of neutrons; the different possible versions of each element are called isotopes.For example, the most common isotope of hydrogen has no neutrons at all; there's also a hydrogen isotope called deuterium, with one neutron, and another, tritium, with two neutrons1H1, deuterium is 2H1, and tritium is 3H1
Hydrogen(stable)
Tritium(radioactive)
Deuterium(stable)
Isotones
Nuclides having the same number of neutrons
80204
82206 and HgPb
• Lead and mercury are isotones with N = 124
Isobars
Nuclides that have the same A’s but different Z’s:
3064
2864 and ZnNi
• Nickel and zinc are isobars with A = 64 and but different Z’s
Nuclear Mass & Biding Energy
Nuclear reactions can be either exothermic (releasing energy) or endothermic (requiring energy to take place)
Energies associated with nuclear changes are usually in the MeV range – 106 times greater than energies associated with the valence electrons involved in chemical reactions
Nuclear Mass & Biding Energy
Energies from exothermic nuclear reactions comes from mass conversion to energyMass loss = ∆m then energy released, E:
2)( cmE ∆=
Atomic mass units (amu) & Energy (MeV)
By definition: 12C atom has a mass of exactly 12 amu
Since its gram atomic weight is 12 g:
MeVergMeVergamu
ergamuscmc
gamu
48.931106.1
)(1049.11
1049.1)103)(1066.1(1/103ith relation wEinstein using
1066.11002.6
11
6
3
321024
10
2423
=×
×=
×=××=
×=
×=×
=
−
−
−−
−
Mass Defect
Is the difference between the atomic mass (measured mass) sometimes called isotopic mass, M, and the mass number, A:
AM −=∆
Mass DefectActually, the mass of a proton is 1.00728 amu; a neutron is 1.00866 amu; a electron is 0.0005485 amu. The standard is that one atom of carbon 12, the isotope of carbon with 6 protons, 6 neutrons, and 6 electrons, has a mass of exactly 12 amu. If you add up 6 protons, 6 neutrons and 6 electrons, you get more than 12 amu:
The mass of 6 protons, 6 electrons, and 6 neutrons is 12.0956 amu, to be precise--but the mass of a carbon nucleus is less than the sum of its parts.
0956.12)00866.1(6)00728.1(6 =+
Binding energyThe "binding energy" of a particular isotope is the amount of energy released at its creation; You can calculate it by finding the amount of mass that "disappears" and using Einstein's equation. The binding energy is also the amount of energy you'd need to add to a nucleus to break it up into protons and neutrons again; the larger the binding energy, the more difficult that would be.
Binding EnergyFor the Nuclide of 11Na24 the total mass in AMU is:
199.24)00055.0(11)00866.1(13)00728.1(11 =++
From appendix D, ∆ = -8.418 MeV = 0.0090371 AMU = M-A
So, M=24-0.0090371=23.991AMUBE = 24.199-23.991 = 0.208AMU = 194 MeVThis is the total BE of the atom – nucleons +
electronsBE/nucleon = 194/24 = 8.08 MeV
Radioactivity
The property that some atomic species, called radionuclides, have of undergoing spontaneous nuclear disintegrationAll of the heaviest elements are radioactive209Bi83 is the only stable nuclide with Z > 82
Radionuclide
May emit alpha or beta particles when the ratio of neutrons or protons is unfavorable for the state of stabilityIf after the emission of the particle, the nuclide is still in an energetically unstable state, it may emit gamma rayNuclear emissions have high kinetic energy (MeV)
Unit of Radioactivity
Becquerel = 1 disintegration per secondIt measures only the rate of nuclear transformationIt does not deal with kinetic energy released in the process
Nucleus Decay
In nuclear decay, an atomic nucleus can split into smaller nuclei. A bunch of protons and neutrons divide into smaller bunches of protons and neutrons
Particle DecayIt refers to the transformation of a fundamental particle into other fundamental particles. The end products are not pieces of the starting particle, but totally new particles.
Types of radiationAlpha particles are helium nuclei (2 p, 2 n):
Beta particles are speedy electrons:
Gamma radiation is a high-energy photon:
p npn
Differences among RadiationCan be distinguished by a magnetic field The positively-charged alpha particles curve in one direction, The negatively-charged beta particles curve in the opposite direction, The electrically-neutral gamma radiation doesn't curve at all.
Alpha DecaySome heavy isotopes decay by spitting out alpha particles. These are actually helium 4 nuclei--clumps of two neutrons and two protons each. A typical alpha decay looks like this:
238U92 => 234Th90 + 4He2
Alpha Decay
Heavy elements with Z>83
αα ∆−∆−∆=
−−=+→
Dp
NHeNRnNRa
QMMMQ
HeRnRa
,,,
42
22286
22688
daughterparent
Use Appendix D to find these values
Energy QIt is shared by the alpha particle and the recoil (daughter) nucleusParent nucleus was at rest, so the momenta of the 2 decay products must be equal and opposite:
QMVmv
MVmv
=+
=
22
21
21
Recoil nucleus
Alpha particle
Eα and EN
QEEMm
mQMVE
MmMQmvE
MmmMQv
N
N
=++
==
+==
+=
α
α
2
2
2
2121
)(2
Beta Decay-electron
Suppose an atom has too many neutrons to be stable.In beta decay, a nucleus simultaneously emits an electron, or negative beta particle
That's the case with tritium, 3H1. 3H metamorphoses into helium 3, it also gives off an electron--which has hardly any mass, and is endowed with a negative charge that exactly cancels one proton.
3H1 => 3He2 + 0e-1The nuclear reaction involved in the beta decay of tritium by giving the electron a "mass number" of 0 and an "atomic number" of -1
•Note that the mass & charges are concerved•It must be true in any nuclear reaction!!
Beta Decay
A nucleus simultaneously emits an electron, or negative beta particle and an antineutrino
Beta decayBeta decay can be seen as the decay of one of the neutrons to a proton via the weak interaction
Weak interaction diagram
Beta Decay
A nucleus simultaneously emits an electron, or negative beta particle and an antineutrino
Dp
NiNNiCoNCo
NNiNCo
QmmMmMQ
mMMQvNiCo
∆−∆=
−+−+=
+−=++→
−
−
β
β
)28(27)(
,,
,,
00
01
6028
6027
Note that here we are neglecting the differences in atomic-electronBEs
Energy QIt is shared by the beta particle, antineutrino and the recoil (daughter) nucleusThe nucleus, because of its large mass, receives negligible energy
These are initial kinetic energies of the electron and antineutrino
QEE v =+−β
Beta Decay-positron
Suppose an atom has not enough neutrons to be stable.In beta decay, a nucleus simultaneously emits an positron, or positive beta particle
That's the case with beryllium 7, 7Be4 - It decays to lithium 7--so a proton turns into a neutron
So a positron is emitted--a particle that's just like an electron except that it has opposite electric charge. In nuclear reactions, positrons are written this way: 0e1
7Be4 => 7Li3 + 0e1•Note that the mass & charges are concerved•It must be true in any nuclear reaction!!
Positron Decay
A nucleus simultaneously emits a positron, or positive beta particle and a neutrino
2
,,
,,
00
01
2210
2211
2
2)10(11
mcQ
mmMmMQmMMQ
vNeNa
Dp
NeNNeNaNNa
NNeNNa
+∆−∆=
−+−+=
−−=++→
+β
β
Positron Decay
For positron emission to be possible:The mass of the parent atom must be greater than that of the daughter by at least
MeVmc
mcDp
022.12
22
2
=
+∆>∆
Gamma-rayAfter alpha or beta decay, a nucleus is often left in an excited state--that is, with some extra energy. It then "calms down" by releasing this energy in the form of a very high-frequency photon, or electromagnetic wave, known as a gamma ray.
Gamma Ray
One or more gamma rays can be emitted from the excited states of a daughter nuclei following radiation decayTransition that results in gamma emission leave Z and A unchanged and are called isomericNuclides (initial and final states) are called isomers
Gamma Rays
MeVQQ
vBaCs
Dp
1.10.889.86
00
01
13756
13755
=+−=
∆−∆=++→ − β 55Cs137 1.174
1.174
5%
β−
β−
γ 85%
0.662
056Ba137
0.51295%
From appendix:Decay by this mode take places 5% of time – releasing 1.174 MeV95% of the cases leaves the daughter nuclei in an excited state with energy 1.174-0.512=0.662 MeVA photon with this energy is shown with 85% frequencyInternal conversion occurs in 95-85=10% of the disintegrationBa X-rays are emitted following the inner-shell vacancies created in the atom by internal conversion
Internal ConversionIs the process in which the energy of an excited nuclear state is transferred to an atomic electron, a K or L shell electron, ejecting it from the atomThis process is not the same as emitting a gamma ray which knocks an electron out of the atom It is also not the same as beta decay, since the emitted electron was previously one of the orbital electrons, whereas the electron in beta decay is produced by the decay of a neutron.
Internal Conversion Coefficient
The ratio of the number of conversion electrons Ne to the number of competing gamma photons Nγ for the transition:
γ
αNNe=
Kinetic Energy of Ejected Atom
Ee is equal to the excitation energy E*of the nucleus minus the binding energy EB of the electron in its atomic shell:
Be EEE −= *
Decay by Electron CaptureSome nuclei undergo a radioactive transformation by capturing an electron from the K shell and emitting a neutrinoThe neutrino acquires the entire energy Q released by the reaction
BDp
BDpEC
NRhBNPd
m
EEQ
MEmMQvRmePd
m
>∆−∆
+∆−∆=
−−+=+→+−
,,
00
10345
01
10346
Decay by Electron CaptureAn atom with too few neutrons may gain one more neutron by capturing one of the negatively charged electrons orbiting about the nucleus. This effectively cancels the positive charge on one of the protons, turning it into a neutron. An example of this kind of radioactivity is the decay of beryllium-7 to form lithium-7 Be7 + e- Li7
