1.2 Basic Principles of Nuclear Physics

Home , Isotone

Nucleus consists of:

Z protons with e+ charge N neutrons with no charge. A Mass number A=Z+N

protons & neutrons are bound by strong force: R≅10-13 m Isotope, Isobar, Isotone

Isotopes: nuclei with Z=constant, N varies!

Isotones: nuclei with N=constant, Z varies! Isobars: nuclei with A=constant, Z,N varies! hydrogen isotopes: Z=1

Z Nuclear Chart

Â Isotope Â Isobar

Ã Isotone N Nuclear Masses & Energetics

E=m · c2

The mass M of the nucleus is smaller than the mass of its proton and neutron constituents!

2 2 2 M · c < Z mp ·c + N mn ·c The mass difference is the binding energy B

The binding energy is the energy that needed to dissociate a nucleus into its single constituents or that is released when N neutrons and Z protons fusion together to form nucleus with mass number A! example

-24 mp= 1.007596 · 1.66 · 10 g -24 mn= 1.008486 · 1.66 · 10 g

M(18O) = 17.99916 · 1.66 · 10-24 g Z=8, N=10

2 B = (Z · mp+ N · mn-M) ·c B(18O) = 1.382 · 105 keV

Atomic Mass Unit: 1 amu=1/12(M12C)=1.66 · 10-24 g Energy Diagrams

Ex 15.94 MeV 17N+p

8.04 MeV 17O+n 6.23 MeV 14C+α

18O Break-Up of 18O into 14C+α requires 6.23 MeV; Fusion of 14C+α releases 6.23 MeV (excited 18O); energy release by γ-emission to ground state of 18O Reaction Channels

Ex 15.94 MeV 17N+p

8.04 MeV 17O+n 6.23 MeV 14C+α

18O Break-Up of 18O into 17N+p requires 15.94 MeV; Fusion of 17N+p releases 15.94 MeV (excited 18O); energy release by γ-emission to ground state of 18O 17 or by n emission to O: En=15.94MeV-8.04MeV=7.9MeV 14 or by α emission to C: Eα=15.94MeV-6.23MeV=9.7MeV Nuclear Reaction Processes

In a nuclear reaction two nuclei combine forming a third nucleus! The total number of protons and neutrons remains constant! 17O+n ⇒18O; 17N+p⇒18O; N=9+1⇒N=10; N=10+0⇒N=10; Z=8+0⇒Z=8; Z=7+1⇒Z=8; The third nucleus is called compound nucleus. It either decays by γ-emission to ground state or breaks up by particle emission into light particle component (e.g. α)and heavy rest nucleus (14C).

17O(n,γ)18O capture reaction 17N(p,γ)18O 17O(n,α)14C transfer reaction 17N(p,α)14C charge exchange 17N(p,n)17O Reaction and Decay Processes Reaction Q-values • Mass difference between initial particles and final particles is called: Q-value (energy) • If a reaction needs energy to take place it is called: Endothermic (Q<0) • If a reaction releases energy when taking place it is called: Exothermic (Q>0) 2 A(a,b)B (mA+ma-mB-mb)·c =Q

a (p, n, α) http://ie.lbl.gov/toimass.html http://nucleardata.nuclear.lu.se/database/masses/

A (17N, 17O, 14C) Nuclear Decay & Radioactivity Nuclei are only in certain Z,N configuration stable (minimum of energy E=mc2 ) Otherwise nucleus ‘decays’ by particle or radiation emission to energetically more favorable configuration!

Nucleus can be displayed Decay occurs in terms of a from excited level scheme state or ground like atom state configuration (nuclear shell model) Conversion process associated with radioactive decay The α-Decay Alpha Decay of the Nucleus

Occurs mainly for very heavy nuclei which are not stable against alpha emission

Alpha particle α = 4He

226 222 4 88 Ra ⇒+86Rn 2He Nucleus conversion through α-decay

A A−4 N Determine the end-product of the ‘yellow’ α-emitter: Z XXNZ⇒+−2 N −2 α Beta Decay of the Nucleus

β decay is the emission of an electron e- or positron e+ to convert neutron to proton or proton to neutron inside nucleus

6 · e+ Ö 7 · e+ +1 · e- Too many protons The β decay always converts along isobars Too many neutrons Nucleus conversion through β+,−-decay Z

+ A A + Determine the end-product of the β -emitter: Z XXNZ⇒+−+11N β

− A A − Determine the end-product of the β -emitter: Z XXNZ⇒++−11N β The β-Decay Gamma Decay of Nucleus

excited states in nucleus

γ emission Excitation of nucleus λ<10-15 m with subsequent characteristic γ emission

Ex Excited states correspond to vibration, rotation or quantum state excitation The γ-Decay Radioactive Decay Laws dN N: number of radio-isotopes =−λ ⋅N dt Radioactive substance dN =−λ ⋅dt N

−⋅λ t Nt()=⋅Nt(0 )e

λ: decay constant

N(t0)=N0: initial number of radio-isotopes Half-Life of Radio-Isotope time (days) 131I (%) 0 100.0000 −⋅λ t 1 91.7411 Nt()=⋅N e 2 84.1642 0 3 77.2132 4 70.8362 decay curve 5 64.9859 6 59.6188 7 54.6949 100 8 50.1777 9 46.0335 80 10 42.2317

] 131 15 27.4446 I

[% 60 20 17.8351 (t)

25 11.5903 N T = 8.04 d 40 1/2 30 7.5321 40 3.1809 50 1.3434 20 60 0.5673 70 0.2396 0 80 0.1012 0 1020304050 90 0.0427 time [days] 100 0.0180 T1/2 Half-Life and Decay Constant

1 −⋅λ T1 2 The decay constant λ NT()1 ==N00N ⋅e 2 2 is inverse proportional to the half-life T1/2 ln 2 =⋅λ T1 2

ln 22ln Half-life of a radioactive λ ==T1 substance determines a T1 2 λ 2 time-scale Ö clock Radioactive Clocks

dating isotopes Example: If your 22920 year old sample (4 half-lives) originally 14 100 had 1000 C isotopes, how many T (226Ra)=1600 y 14C isotopes are left today? 80 1/2 226Ra ]

% 14 14C T1/2( C)=5730 y [ 60 y −⋅λ 22920[]y it Ny([22920 ])=⋅1000 e iv t

c 40 a −−41 λ ==ln2 5730[yy] 1.21⋅10 [] 20 Ny([22920 ])= 62 0 0 10000 20000 30000 40000 time [years] Units for scaling the decay

dN decays Classical Unit: 1 Curie [Ci] 10   1[]Ci = = 3.7⋅10   dt  s 

dN decay Modern Unit: 1 Becquerel [Bq] 1[]Bq = =1   dt  s 

The so-called dosimetry units (rad, rem) determine the amount of damage radioactive radiation can do to the human body. They depend on the kind and nature of the incident radiation (X-rays, γ-rays, α-particles, β-particle, or neutrons). It also depends on the energy loss of the particular radiation and the associated ionisation effects in the human body material. Radiation Detection Example: Dosimetry

E Amount of energy E deposited Dose: D = by radiation into body part m of mass m. unit Rad or Gray Radiation independent dose Equivalent Dose: HQ=⋅DQ is normalization factor Unit Rem or Sievert Photons: Q=1 Neutrons: E<10keV Q=5 Neutrons: E>10keV Q=15 Protons: Q=5 Alphas : Q=20 Risk Factors of Radiation UNITS OF RADIATION MEASUREMENT Dosage units:

The Sievert (Gray) is a measure of biological effect. 1 Gray (Gy) = 1 Joule/kg (Energy/mass) 1 Sievert (Sv) = Gray x QF, where QF is a "quality factor" based on the type of particle. QF for electrons, positrons, and x-rays = 1 QF = 3 to 10 for neutrons, protons dependent upon the energy transferred by these heavier particles. QF = 20 for alpha particles and fission fragments.

Converting older units: 1 rad = 1 centigray = 10 milligrays ( 1 rad = 1cGy = 10 mGy ) 1 rem = 1 centisievert = 10 millisieverts ( 1 rem = 1cSv = 10 mSv )

Nominal background radiation absorbed dose of 100 mrad/year = 1 mGy/yr. Nominal background radiation dose biological equivalent of 100 mrem/year = 1mSv/yr. Occupational whole body limit is 5 rem/yr = 50 mSv/yr. 2.5 mrem/hr or 25 uSv/hr is maximum average working level in industry.

Exposure rate from Naturally Occurring Radioactive Material; an empirically derived conversion factor for Ra-226 decay series: 1.82 microR/ hour = 1 picoCurie/gram.