Transcript Topic 7_2_Ext B__Nuclear stability

Topic 7.2 Extended
B – Nuclear Stability
NUCLEON POPULATIONS
Stable isotopes exist for
elements having atomic numbers
Z = 1 to 83, excepting 43 and
61.
Up to Z = 20, the neutronproton ratio is close to 1.
Beyond Z = 20, the neutronproton ratio is bigger than 1,
and grows with atomic number.
Since  decay decreases
protons and neutrons at the
same rate, the daughter
nucleus would be no more
stable than the parent, for
the larger atomic numbers.
Thus the larger unstable nuclei
become stable by a combo  decay
and - decay (which turns
neutrons into protons).
FYI: Since there are 6 more neutrons than protons, sulfur-38 is
susceptible to - decay.
Question:
Topic 7.2 Extended
How many - decays would it undergo?
B – Nuclear Stability
whichOF
element
would
it transmute?
PQuestion:
AIRING ETo
FFECT
STABLE
NUCLEI
There are 168 stable nuclei having an even number of
protons and neutrons.
There are 107 stable nuclei having either Z even
and N odd, or Z odd and N even.
There are only 4 stable nuclei having an odd number
of each.
26
Thus, you would expect 27
13Al to be stable, but 13Al to
be unstable, and this is the case.
General Criteria for Nuclear Stability
(1) Isotopes with Z < 83 are stable.
(2) Most Even-Even, Even-Odd, Odd-Even isotopes are stable.
(3) Isotopes with Z < 20 are stable if Z = N. Else N > Z.
Is sulfur-38 stable, or is it unstable?
Since Z = 16 < 83 for sulfur, (1) is satisfied.
Since N = 38 - 16 = 22, and Z = 16, (2) is satisfied.
Since Z < 20 and N  Z (3) is not satisfied.
We may conclude that sulfur-38 is NOT stable.
FYI: 1H has one proton, and 1 electron for a total mass of 1.00727 u +
0.000548 u = 1.007818 u. This value matches the value in the table:
Topic 7.2 Extended
FYI:
has two
(which includes the 2 electrons) and 2 neutrons,
B
– Nuclear Stability
for a total mass of 2(1.007825) + 2(1.008665) = 4.03298 u. This
4He
1H
Bvalue
INDING
ENERGY
DOES
NOT match the value in the table:
In the world of nuclear reactions we have to keep
FYI: The DIFFERENCE between the constituent masses and the
track of the mass of the nucleus4 if we are to
resulting mass
is called
the mass
He has a mass defect of
determine
the
energy
of a defect.
reaction.
0.030377
u. unified atomic mass unit
4.03298
To this- 4.002603
end we =define
the
(u) using a neutral carbon-12 atom as our standard
of precisely 12.000000 u.
Thus
1 u = 1.660610-27 kg
Atomic Mass Unit (u)
Particle Masses and Energy Equivalents
Particle
Mass (u)
Mass (kg)
Energy (MeV)
1u
1.660610-27
931.5
Electron
0.000548
9.109510-31
0.511
Proton
1.00727
1.6726510-27
938.28
1H
atom
1.007825
1.6735610-27
938.79
Neutron
1.008665
1.6750010-27
939.57
4He
4.002603
6.6467210-27
3738.8
atom
FYI: This energy deficit is called the total binding energy (Eb) of the
helium nucleus. In fact, this is the energy released in the nuclear
Topic 7.2 Extended
reaction which combines the nucleons to form helium.
B – Nuclear Stability
FYI: The sun generates its energy through the nuclear reaction
Bcombining
INDING ENERGY
hydrogen into helium. Each reaction liberates 28.3 MeV.
We can convert the mass defect m into equavalent
energy using E = mc2:
0.030377 u 1.660610-27 kg ( 3108 ms-1 )2
E =
1 u
1 eV
4.540010-12 J
E =
1.610-19 J
E = 28.375 MeV
To save time you can use the conversion from mass
to MeV:
1 u = 931.5 MeV
Atomic Mass Unit (u)
Thus
E =
0.030377 u
Eb = mc2
931.5 MeV
1 u
= 28.30 MeV
Binding Energy (Eb)
FYI: The energy to ASSEMBLE the 4He nucleus from hydrogen on the
sun is from gravitational compression. Causing fusion here on earth,
Topic 7.2 Extended
we have to obtain this energy in a different way.
B – Nuclear Stability
FYI: The energy to DISASSEMBLE the 4He nucleus can come from
BINDING ENERGY
photons of very high energy, or particle beams such as electrons,
Just as 28.3 MeV are
protons, or anti-protons (p-bars).
released when the 4He
fuses...
FUSION
... we can reverse
the process if we
somehow "inject"
28.3 MeV into the
helium nucleus:
FISSION
FYI: This is why nuclear
bombs7.2
pack aExtended
real punch!
Topic
B – Nuclear Stability
BINDING ENERGY
We can calculate the average binding energy per
nucleon for helium (or any stable isotope) using the
following formula:
binding energy per nucleon =
Thus for
4He
Eb
A
Average Binding
Energy
(A = 4) we have
28.3 MeV = 7.075 MeV
Eb
=
4
A
To disassemble the nucleus we would need to supply
7.075 MeV / nucleon.
If we could remove one nucleon, it would take about
7.075 MeV.
FYI: Recall that it takes 13.6 eV to remove an electron from a
hydrogen atom. Compare this CHEMICAL energy to the NUCLEAR
energy of 7,075,000 eV to remove a nucleon.
This gives us a rough comparison NUCLEAR ENERGY to CHEMICAL
ENERGY of 7,075,000 eV / 13.6 eV = 520,221!
FYI: The higher the binding energy per nucleon, the harder it is to
break apart the nucleus. Thus, the bigger Eb/A the more stable the
Topic 7.2 Extended
nucleus. Fe (iron) is the most stable element.
B – Nuclear Stability
BINDING ENERGY
We can calculate the average binding energy per
nucleon for all of the elements:
For the
elements with A
< 56 note that
fusion results
in more stable
nuclei.
For the
elements with A
> 56 note that
fission results
in more stable
nuclei.
Note that iron
is the most
stable element.
Question: Why will it cease fusion when it reaches this point?
Question: If the universe
started7.2
out asExtended
hydrogen and helium, and
Topic
stars can only breed nuclei up to iron, where do all the higher elements
B – Nuclear Stability
come from?
BINDING ENERGY
This brings us to an aside on
stellar evolution:
During the lifetime of a star
there are two opposing forces
maintaining an equilibrium.
(1) Gravitation is trying to
collapse the star.
(2) Radiation pressure is
opposing the gravitational
collapse.
If a star is sufficiency massive,
Gravitational
Collapse
Nuclear
Reactions
Start
it will maintain nuclear reactions
Balanced by Radiation
until it becomes IRON.
Pressure
When such a star becomes iron, it
will have no more radiation
pressure to oppose gravity.
It will collapse (due to gravity), and its complex
iron nuclei will decay into ALL NEUTRONS!
FYI: This is called the IRON CATASTROPHE.
Topic 7.2 Extended
B – Nuclear Stability
MAGIC NUMBERS
Remember how Pauli's Exclusion Principle told us how
many electrons could be at any energy level?
Thus, the magic numbers were 2, 8, 18, 32, etc. for
electrons about a nucleus.
Theoretically, these numbers came from
Schrödinger's equation.
To make a long story short, Schrödinger's equation
also reveals something about the shell structure of
the nucleus!
The shells of the nucleus fill up with nucleons
just like electron shells fill up with electrons.
A nuclear shell is said to be closed if it has the
optimum number of protons OR neutrons in it.
Here is the series of those optimum numbers:
2, 8, 20, 28, 50, 82, or 126.
Magic Numbers
FYI: Nuclei having this many protons (or neutrons) are more stable
than the average nuclei (and usually have more stable isotopes).