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?