Probing the Subatomic World Nucleus consists of protons and neutrons. This explains the existence of isotopes, isobars, isotones, isomers and mirror nuclei. The nucleus: A M Z , e.g. 14 C 6. Z = atomic number, # of protons/electrons
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The nucleus:
AMZ , e.g. 14C6
Z = atomic number, # of protons/electrons
A = atomic mass, total # of nucleons
N = A – Z = number of neutrons
ISOTOPES – nuclides with identical Z
ISOBARS – nuclides with identical A
ISOTONES – nuclides with identical N
ISOMERS – two nuclei of the same species but different
energy states, of which at least one is metastable
MIRROR NUCLEI – proton (neutron) number of one
is the neutron (proton) number of the other
Which are isotopes, isobars, isotones, mirror nuclei?
12B5, 14C6,14N7, 14O8, 16O8
Isobars  14C6,14N7, 14O8
Isotones  12B5, 14N7
Isomers  14O8, 16O8
Mirror nuclei  14C6, 14O8
NUCLEAR SIZE(R. Hofstadter) –mean electromagnetic
radius, i.e. the radius to the 50% point in the
density distribution
Re = (1.07 0.02) A1/3 x 1015 m= 1.07 A1/3 F
1 F (fermi) = 1015 m
What is the mass number of a nucleus having a radius
one third that of 27Al13?
nuclide, leaving latter with two units less charge
and four units less mass number
Geiger counter measures radioactivity
Units:
Curie (Cu) – quantity of any radioactive material giving
3.7 x 1010 disintegrations per minute
Rutherford (rd) – amount of radioactive substance which gives 106 disintegrations per second.
Rutherford and Soddy surmised four families of
radioactive elements
where Ao = original nuclide
N = # of particles emitted
N = # of particles emitted
Z = Zo  2 N+ N
These suggest there might exist 4 different series
of radioactive elements, characterized by a
different value m for the mass numbers of its members
A = 4n + m
Series 4n 4n + 1 4n + 2 4n + 3
Parent nucleus Th232 Np237 Ur238 Ur235
Stable nucleus
Halflife ( T1/2, y) 1.39x106 2.25x106 4.51x109 7.07x108
Series 1 – those with atomic weight being a multiple of 4
e.g. 228, 232, 236
Series 2 – those with atomic weight 4n + 1
e.g. 229, 233, 237
Series 3 – those with atomic weight 4n + 2
e.g. 230, 234, 238
Series 4 – those with atomic weight 4n + 3
e.g. 231, 235, 239
The shell model predicts that nuclei with proton numbers Z or neutron numbers N equal to 2, 8, 20, 28, 50, 82, and 126
are stable. e.g. lead
Halflife
#
time
halflife
Halflife governs the rate of disappearance after it is
isolated from the other members of the family
T1/2 = 0.693/
= disintegration constant; the fraction of atoms
present that decay per unit time
N = No e t
This is a result of the transformation of a neutron
into a proton.
on1 p + e +
The energy spectrum is continuous.
Heines and Cowan verified the existence
of neutrinos using the reaction
P + n + e
Enrico Fermi and Emilio Segre, in 1934 bombarded
uranium with neutrons and found several ray
activities with different halflives
Otto Hahn and Fritz Strassman, in 1938 showed that
One of the radioactive elements in the Fermi/Segre
Experiment was an isotope of barium (56Ba141)
Otto Frisch and Lisa Meitner suggested that uranium was
Undergoing a nuclear fission process:
U235 + n U236 X + Y + neutrons
U236 is a highly unstable isotope
X and Y are fission fragments
X and Y can be either Ba144 and Kr89 or Xe140 and Sr94
Xe decays into Cs, then Ba to La and to Ce
Sr decays into Y and then Zr
The process releases neutrons and heat energy. The heavy
nucleus captures a slow neutron. The Coulomb repulsion
distorts the nucleus within 10exp13 seconds. The nucleus
fragments with the release of prompt neutrons. This may take
only seconds or years delaying the release of neutrons.
Energy released in nuclear fission
Before fission(isotopic mass) After fission (isotopic mass)
U(235) = 235.0439 amu Ce(140) = 139.9054 amu
n = 1.0087 amu Zr (94) = 93.9036 amu
236.0526 amu 2n = 2.0173 amu
6 = 0.0330 amu
235.8296 amu
Mass difference = 0.233 amux931 MeV/amu = 208 MeV
cf. with particle disintegration giving energy = 5 MeV and
chemical combustion process energy of 4 eV.
Fast Breeder – relies on fast, highly energetic neutrons
Fast Breeder – relies on fast, highly energetic neutrons
fp
Pu239

n

fp
U238
U239
Np239
n
n
Disintegration of fertile isotope by fast neutron. The fission process releases heat energy as byproduct.
Definitions of terms and equivalences
Units of Energy: 1 joule (J) = 1 newtonmeter
1 J = 0.738 ftlb = 107 ergs
1 cal = 4.186 J
1 Btu = 252 cal = 1054 J
1 kWh = 3.6 x 10exp6 J
1 barrel of oil (BOE) = 5.8x106 Btu
1 Q = 1018 Btu = 1021 J
= 1.85x1011 BOE
= 3x1014 kWh
Fission (fast breeder) 200
Solar (p.a.) 1000
Geothermal (hot rock) 1000
Fusion (DT) 1x106
(lithium107 tons)
(DD) 3x1010
ENERGY CONSUMPTION
Current consumption = 12 terawatts (85% from
fossil fuels); 1TW=5BBOE
Projected for 9 B population = 27 TW
for 14 B population = 42 TW
ICRP limits of radiation for individuals
Organ or tissue Annual dose limits
(in rem*)
Gonads, red bone marrow 0.5
Skin, bone, thyroid 3.0
Hands & forearms, feet/ankles 7.5
Other single organs 1.5
Whole body (uniform) 0.5
*rem(roentgenequivalent man) measures the dose
equivalent in terms of the absorbed dose in rads =
100 ergs/gram, of energy deposition x quality factor
e.g quality factor of Xrays =1; fast neutrons = 10 and
Alpha particle radiation = 10
3. 3H dating used in problems connected with rainfall and
meteorology, such as relation between ground water
present at a given locality and local rainfall.
4. 7Be used in the study of atmospheric mixing with its 53day
halflife
Hans Bethe suggested in 1938 that a nuclear reaction
in which two nuclei came together to form a single
heavier species plus the release of large quantities of
energy.
Carbon cycle : 1H + 12C 7N +
7N 6C + e +
Threshold Plasma Average energy gain
temperature per fusion*
D + T He(4) + n 10 keV 1800
D + D T + p 50 keV 70
He(3) + n
D + He(3) He(4) + p 100 keV 180
T + He(3) He(4) + 2n + E
1 eV = 11,600 K* ratio of energy released to energy absorbed per reaction
Experimental Requirements for Fusion
1. reaction rate must be high to produce useable quantities of power
2. power by fusion reaction must be greater by an order of
magnitude than the power required to support the reaction
Pfus 3nT/E
Pfus = nDnT Vr (DT) EDT
3nT = thermal energy content of plasma
E = characteristic time in which plasma loses its energy due to
all possible mechanisms such as conduction, convection,
radiation
nDnT = densities of deuterium and tritium components
n = nD + nT = total density
EDT = total energy released per DT fusion reaction
Vr (DT) = total cross section for reactions
Pfus is maximum when nD = nT = n/2
Lawson criterion nE [12T/EDT] /Vr (DT)
If T = 10 keV, EDT = 40 MeV; Vr (DT) = 1023 m3/s
nE 1.5 x 1020 s/m3 (minimum for DT reaction)
nE T 1021 keV s/m3 (triple product)
Courtesy Princeton Univ.
Total Fusion
Power 1.5 Gw
Burn Time 1000 s
Plasma Current
21 MA
Maximum Toroidal
Magnetic Field
5.7 T
Courtesy ITER Program