Nucleus & Nuclear

AGEN-689 Advances in Food Engineering

„ The nucleus of an of Z and number A consist of Z and N = A-Z „ A gives the total # of (protons and neutrons) „ : a species of atom characterized by its nuclear constitution (its value of Z and A (or N)) •Unstable are radioactive: their nuclei change or decay by spitting out radiation, in the form of or electromagnetic waves.

„ Atoms of the same element can have different numbers of neutrons; the different possible versions of each element are called isotopes. „ For example, the most (stable) common of hydrogen has no neutrons at all; there's also a hydrogen isotope called , with one , and Deuterium another, , with two (stable) neutrons Tritium 1 2 „ H1, deuterium is H1, 3 (radioactive) and tritium is H1

„ having the same number of neutrons

206 204 Pb82 and Hg80

and are isotones with N = 124 Isobars

„ Nuclides that have the same A’s but different Z’s:

64 64 Ni28 and Zn30

and 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 involved in chemical reactions Nuclear Mass & Biding Energy

„ Energies from exothermic nuclear reactions comes from mass conversion to energy

„ Mass loss = ∆m then energy released, E: E = (∆m)c2 units (amu) & Energy (MeV)

„ By definition: 12 „ C atom has a mass of exactly 12 amu

„ Since its gram atomic weight is 12 g: 1 1 amu = =1.66×10−24 g 6.02×1023 using Einstein relation with c = 3×1010 cm / s 1 amu = (1.66×10−24 )(3×1010 )2 =1.49×10−3 erg 1.49×10−3 erg(MeV) 1 amu = = 931.48MeV 1.6×10−6 erg Mass Defect

„ Is the difference between the atomic mass (measured mass) sometimes called isotopic mass, M, and the , A:

∆ = M − A Mass Defect

„ Actually, the mass of a is 1.00728 amu; a neutron is 1.00866 amu; a is 0.0005485 amu. „ The standard is that one atom of 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: 6(1.00728) + 6(1.00866) =12.0956

„ 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.

„ The "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 Energy

24 „ For the Nuclide of 11Na the total mass in AMU is: 11(1.00728) +13(1.00866) +11(0.00055) = 24.199

„ From appendix D, ∆ = -8.418 MeV = 0.0090371 AMU = M-A „ So, M=24-0.0090371=23.991AMU „ BE = 24.199-23.991 = 0.208AMU = 194 MeV „ This is the total BE of the atom – nucleons + electrons „ BE/ = 194/24 = 8.08 MeV Radioactivity

„ The property that some atomic species, called , have of undergoing spontaneous nuclear disintegration

„ All of the heaviest elements are radioactive 209 „ Bi83 is the only with Z > 82

„ May emit alpha or beta particles when the ratio of neutrons or protons is unfavorable for the state of stability „ If after the emission of the , the nuclide is still in an energetically unstable state, it may emit „ Nuclear emissions have high (MeV) Unit of Radioactivity

„ Becquerel = 1 disintegration per second „ It measures only the rate of nuclear transformation „ It does not deal with kinetic energy released in the process Nucleus Decay

„ In nuclear decay, an can split into smaller nuclei.

„ A bunch of protons and neutrons divide into smaller bunches of protons and neutrons Particle Decay

„ It 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 radiation

„ Alpha particles are nuclei (2 p, 2 n): p n n p

„ Beta particles are speedy electrons:

„ Gamma radiation is a high-energy photon: Differences among Radiation

„ Can 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.

„ Some 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: 238 234 4 „ U92 => Th90 + He2 Alpha Decay

„ Heavy elements with Z>83

226 222 4 88 Ra→ 86 Rn+2 He

Q = M Ra,N − M Rn,N − M He,N

Qα = ∆ p − ∆ D − ∆α

parent daughter

Use Appendix D to find these values Energy Q

„ It is shared by the and the recoil (daughter) nucleus

„ Parent nucleus was at rest, so the momenta of the 2 decay products must be equal and opposite:

mv = MV Recoil nucleus Alpha particle 1 1 mv2 + MV 2 = Q 2 2 Eα and EN

2MQ v2 = m(m + M ) 1 MQ E = mv2 = α 2 m + M 1 mQ E = MV 2 = N 2 m + M

Eα + EN = Q -electron

„ Suppose an atom „ That's the case with tritium, 3H . has too many 1 3 „ H metamorphoses into helium neutrons to be 3, it also gives off an electron-- stable. which has hardly any mass, and is endowed with a „ In beta decay, a negative charge that exactly nucleus cancels one proton. 3 3 0 „ H => He + e simultaneously emits 1 2 -1 „ The involved an electron, or in the beta decay of tritium by negative beta giving the electron a "mass •Note that the mass & chargesnumber" are concervedof 0 and an "atomic number" of -1 particle •It must be true in any nuclear reaction!! Beta Decay

„ A nucleus simultaneously emits an electron, or negative and an antineutrino Beta decay

„ Beta decay can be seen as the decay of one of the neutrons to a proton via the Weak interaction diagram Beta Decay

„ A nucleus simultaneously emits an electron, or negative beta particle and an antineutrino

60 60 0 0 27 Co→28 Ni+−1β +0 v

Q = M Co,N − (M Ni,N + m)

Q = M Co,N + 27mCo − (M Ni,N + 28mNi ) − m

Q − β = ∆ p − ∆ D

Note that here we are neglecting the differences in atomic-electron BEs Energy Q

„ It is shared by the beta particle, antineutrino and the recoil (daughter) nucleus

„ The nucleus, because of its large mass, receives negligible energy

E − + E = Q β v

„ These are initial kinetic energies of the electron and antineutrino Beta Decay-

„ Suppose an atom „ That's the case with 7, 7Be - It decays to has not enough 4 7--so a proton turns into a neutrons to be neutron

stable. „ So a positron is emitted--a particle that's just like an „ In beta decay, a electron except that it has nucleus opposite . In simultaneously emits nuclear reactions, are written this way: 0e an positron, or 1 7 7 0 „ Be => Li + e positive•Note beta that the particle mass & charges are concerved4 3 1 •It must be true in any nuclear reaction!! Positron Decay

„ A nucleus simultaneously emits a positron, or positive beta particle and a

22 22 0 0 11 Na→10 Ne+1β +0 v

Q = M Na,N − M Ne,N − m

Q = M Na,N +11mNa − (M Ne,N +10mNe ) − 2m 2 Qβ + = ∆ p − ∆ D + 2mc Positron Decay

„ For to be possible:

„ The mass of the parent atom must be greater than that of the daughter by at least 2 ∆ p > ∆ D + 2mc 2mc2 =1.022MeV Gamma-ray

„ After alpha or beta decay, a nucleus is often left in an --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 decay

„ Transition that results in gamma emission leave Z and A unchanged and are called isomeric

„ Nuclides (initial and final states) are called isomers Gamma Rays

137 137 0 0 Cs137 55 Cs→ 56 Ba+−1β +0 v 55 1.174

Q = ∆ p − ∆ D 0.512 1.174 β− 95% Q = −86.9 + 88.0 =1.1MeV 0.662 5% „ From appendix: „ Decay by this mode take places 5% of time – releasing 1.174 MeV β− γ „ 95% of the cases leaves the daughter 85% nuclei in an excited state with energy 1.174-0.512=0.662 MeV „ A photon with this energy is shown with 85% frequency 137 56Ba 0 „ occurs in 95- 85=10% of the disintegration „ Ba X-rays are emitted following the inner-shell vacancies created in the atom by internal conversion Internal Conversion

„ Is 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 atom „ This 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 Ne to the number of α = competing gamma N photons Nγ for the γ transition: 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:

Ee = E *−EB Decay by

„ Some nuclei undergo a radioactive transformation by capturing an electron from the K shell and emitting a neutrino „ The neutrino acquires the entire energy Q released by the reaction

103 0 103m 0 46 Pd+−1e→ 45 Rm+0 v

Q M m E M m = Pd ,N + − B − Rh,N

QEC = ∆ p − ∆ D + EB

∆ p − ∆ D > EB Decay by Electron Capture

„ An 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- Æ Li7