Nuclear Physics Recap, Lecture notes of Particle Physics

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• © Matthias Liepe,
• Recap I Lecture

Recap II

Nuclear Physics: The Nucleus

• Positive charge and most of the atom’s mass are concentrated in a tiny dense core of ~ 10-15^ m to 10-14^ m in diameter. -> Atomic nucleus
• Nuclei are composed of protons (charge = +e per proton) and neutrons (no electric charge) - Z = # of protons - N = # of neutrons - Atomic mass number: A = Z + N

• Most nuclei are spherical (some are ellipsoidal):

-> Effective radius: where R 0 ≈ 1.2  10 -15^ m = 1.2 fm

(1 femtometer = 1 fermi = 1 fm = 1  10 -15^ m )

• Element type and chemical properties are determined by Z****.
• Different species (as determined by Z and A ) are called nuclides.

1 / 3

R  R 0 A

• The black shading

indicates the band of

stable nuclides.

• Low-mass, stable

nuclides have

essentially equal

numbers of neutrons

and protons.

• More massive nuclides

have an increasing

excess of neutrons.

Plot of known Nuclides:

• Most nuclides are not

stable and undergo

radioactive decay by

emitting radiation and

transferring into other

nuclides.

• There are no stable

nuclides with Z>

(bismuth).

Plot of known Nuclides:

Radioactive Decay:

• Most nuclides are not stable & undergo radioactive decay by emitting radiation & transforming into other nuclides.
• Radioactive decay is a statistical process
• Decay constant  :
  •  = probability that a particular nuclide will decay in

a unit time interval; [  ] = 1/s

•  = fraction of nuclei in a large sample that are expected to decay on average per unit time interval
•  has a characteristic value for every radionuclide.
•  is independent of any external influence, including the decay of another nucleus.

Radioactive Decay:

• If a sample has N radioactive nuclei of a given type then

the average number decaying per unit time is  N.

 Define decay rate R as:

 Integrate to number of radioactive nuclei vs. time:

with N(0) = number of radioactive nuclei at t = 0  Number of radioactive nuclei decreases exponentially with time constant:

   N average number of decaysper time

dt

dN

R 

 t t  N t N e N e

  ( )  ( 0 )  ( 0 )

1 

Application: carbon-14 dating:

• Carbon-14 ( ) is an unstable isotope of carbon ( ) which is produced in the upper atmosphere by cosmic ray neutrons colliding with :

146 C

T 1 2  5730 years (^147) N (^147) N  n  (^146) C  p

• This 14 C is rapidly oxidized to 14 CO 2 and thus can enter living organisms through photosynthesis & the food chain.
• In the atmosphere, 10.. [ CO ]

[ CO ] 12

2

12

2

(^14)  

• A living organism that derives its carbon from the atmosphere will have the same [^14 C][^12 C] in its tissues.
• But once the organism dies it stops taking in carbon & the amount of 14 C in its tissues decreases due to radioactive decay:  (^146) C  147 N  

T 1 2  5730 years,

• 14 C dating may be complicated because the proportion of 14 C in the atmosphere has not been constant. So, other dating techniques are often used as ‘calibrations’ for 14 C dating.
• Modern human activity has altered the [^14 C][^12 C] in the atmosphere through nuclear weapons tests & the burning of fossil fuels.

Application: carbon-14 dating:

• By measuring the ratio of [^14 C][^12 C], it can be determined how long it has been since the organism died.
• Because the 14 C dating method is good for ages   50,000 years.

Absorbed dose = radiation energy absorbed by an object

per unit mass

Units: 1 grey = 1 Gy = 1 J/kg = 100 rad

Example: Radiation dose from natural sources per year:

~ 2 mGy = 0.2 rad

Radiation Dosage:

The Nuclear Force:

Protons repel each other because of their charge (electric force).

 A totally different attractive force must bind protons & neutrons together in the nucleus. This nuclear force is thought to be a secondary effect of the strong force that binds quarks together to form neutrons & protons.

 The nuclear force must be a very short range force because its influence does not extend far beyond the nuclear “surface”.

• The atomic mass unit:

The atomic mass unit, u, is chosen so that the atomic (not nuclear) mass of 12 C is exactly 12 u.

Atomic mass is often reported in these atomic mass units.

1 u  1. 661  10 ^27 kg.

1 u 931. 494013 MeV/ c^2.

The "curve of binding energy":

A graph of binding energy per nucleon of common isotopes.

More tightly bound.

binding energy per nucleon,

E BEn

[MeV]

Number of nucleons in nucleus (A)

The Nickel nuclide 62 Ni has the highest binding energy per nucleon.

Nuclear reactions:

• Conserved quantities are electric charge & total number of nucleons.
• The energy Q released in a reaction is:

2 2 f

2

Q  m i c  m c   mc

where m i is the total mass of the reactants and m f is the total mass of the products.

• Recall: E = mc^2 , so can convert mass to energy!
• Q  0 when some mass is converted to energy.