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NucleaNuclear r
PhysicPhysicss
What is going on in
there?
Nuclear structureNuclear structureA – atomic mass numberZ – atomic number (number of protons)N – number of neutrons (N = A – Z)X – element symbol (ex. He for helium)
XAZ
example
What element is this?How many protons does it have?How many neutrons does it have?
Kr8436
Strong nuclear Strong nuclear forceforce
Fundamental forceStrong enough to overcome the electrostatic repulsion of the protons – binds nucleus togetherShort range (< 10-15 m) – (this will explain why large nuclei can be unstable)
Binding EnergyBinding EnergyThe nucleus has slightly smaller mass than the sum of its parts…Call this “missing mass” the Mass defect (m)
1 u is equivalent to 931.5 MeV
2)( cmE
example
Use the mass table to calculate the mass of 8 protons (same as atomic mass of hydrogen)Use the mass table to calculate the mass of 8 neutronsTotal these two results. Compare this total to the mass of the oxygen nucleus:
(15.994915 u)Difference is mass defect = binding energy
Binding energy curve
Stability
RadioactivityRadioactivity
As nuclei get larger, the neutrons help provide stability because they contribute to the strong force, but do not have charge to push the nucleus apartBUT – strong force has limited range (< 10-15 m), so as nucleus gets beyond this size adding more nucleons makes it unstable
10-15 m
Notice that Fe is most stable
Modes of decay
decay – a 42He is ejected
from the nucleus decay – an electron (0
-1e) is ejected from the nucleus decay – a high-energy photon is emitted as a nucleon changes nuclear energy levels
- GIRL
- BOY
- MAN
Example
In the fission of 238U energy is released as KE and gamma ray ()Use the mass tables to determine the energy released in this reaction
HeThU 42
23490
23892
example
ePaTh 01
23491
23490
example
RaRa 22688
*22688
Radioactive Decay• The rate of decay is proportional to the number of nuclei
•The half-life is the time for ½ of the sample to decay
Ndt
dN
teNN 0
When N/N0 = ½,
we get
t½ = ln(2)/teAA 0
ln(AB) = ln(A) + ln(B)
ln(A/B) = ln(A) – ln(B)
example
The half-life of 14C is 5730 yr (1.81 x 1011 s).
What is the decay constant for 14C?
Bones of a woolly mammoth have 30% of what would be present in a live animal. How long ago did the animal live?