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6.1.3.
Nuclear Theory & Radioactivity <CJ chap 31 >
6.1.3.1.
Discussion (
)
6.1.3.1.1.
Nucleons
are protons or neutrons – the particles that make up the nucleus of the
atom
6.1.3.1.1.1.
The neutron was discovered in 1932
by Chadwick with a mass slightly larger than the proton
6.1.3.1.1.2.
The atomic number, Z =the number of
protons, and A the mass number = the number of nucleons
6.1.3.1.1.2.1.
A
nucleus is written as
where X is the chemical element corresponding to Z
6.1.3.1.1.2.2.
Isotopes
are nuclei with the same number of protons but differing numbers of neutrons
6.1.3.1.1.2.3.
The
nuclear forces felt by both the p and n are essentially identical
6.1.3.1.1.2.4.
The
binding energy is the amount of energy needed to separate the nucleons
6.1.3.1.1.2.5.
The
mass defect is the binding energy expressed in mass equivalence via E = mc2
6.1.3.1.1.2.6.
The
binding energy per nucleon is greatest in mid-range of A (Fe) and less in Li
and U
6.1.3.1.1.3.
Nuclear reactions:
6.1.3.1.1.3.1.
Rutherford
(1919) observed the first ‘transmutation of an element’ with a + N -> O + H
6.1.3.1.1.4.
Radioactivity is the decay or
disintegration of an unstable nucleus
6.1.3.1.1.4.1.
a decay: The emission of
an alpha particle or He nucleus (2p+2n) – easy to stop
6.1.3.1.1.4.1.1.
Example of a decay
->
+
+ 4.3 MeV
of energy
6.1.3.1.1.4.2.
b decay: The emission of
an electron (or positron) via n -> p + e- +
- not hard to stop
6.1.3.1.1.4.2.1.
Example of b decay
->
+
6.1.3.1.1.4.3.
6.1.3.1.1.4.4.
g decay: The emission of a high
energy photon releasing energy – needs lead to stop
6.1.3.1.1.4.5.
n
decay: The emission of a neutron directly from the nucleus
6.1.3.1.1.4.6.
Half-life
is the time required for half of a substance to undergo disintegration
6.1.3.1.1.4.7.
Radioactive
dating: Carbon 14 has a half life of 5730 years
6.1.3.1.1.4.8.
The
Becquerel (Bq) is the unit of radioactivity = 1 disintegration per sec
6.1.3.1.1.4.8.1.
The Currie (Ci) is another unit of
activity: 1 Ci = 3.70E10 Bq = 1 gr of pure
radium
6.1.3.1.1.5.
Biological Effects of Radiation
6.1.3.1.1.5.1.
Ionizing
radiation (charges particles or g) knocks electrons from atoms &
damages cells
6.1.3.1.1.5.1.1.
The SI unit of ionizing radiation is
the Coulomb per kg or C/kg
6.1.3.1.1.5.1.2.
The Roentgen (R) = 2.58E-4 C/kg is a more common historical unit
6.1.3.1.1.5.2.
Yet
this measures only the ionization effect and not the effect on tissue for which
we use:
6.1.3.1.1.5.2.1.
Absorbed Dose = (Energy absorbed) /
(Mass absorbing) unit = Grey (Gy)=J/kg
6.1.3.1.1.5.2.2.
Radiation Absorbed Dose (RAD) = 0.01
Gy is another common unit
6.1.3.1.1.5.3.
To
compare the damage of absorbing different kinds of radiation we define:
6.1.3.1.1.5.3.1.
Relative Biological Effectiveness
(RBE) = (Dose of 200KeV X-rays Effect) / (Dose )
6.1.3.1.1.5.3.2.
Then Biologically Equivalent Dose
(rems) = Absorbed Dose (in rads) x RBE
6.1.3.1.1.5.3.2.1.
rem
stands for roentgen equivalent man
6.1.3.1.1.5.3.2.2.
Humans
receive an average dose of 360 mrem/yr from all
sources
6.1.3.1.1.5.3.2.3.
(cosmic
rays 28, earth 28, internal 39, Radon 200, Medical/dental 43,..
6.1.3.1.1.5.3.2.4.
The
general population should not get more than 500 mrem / yr
6.1.3.1.1.5.3.2.5.
Workers
should not get more than 5 rem / year (eg dental assistant)
6.1.3.2.
Mathematical
6.1.3.2.1.
The
approximate radius of the nucleus is r = 1.2E-15 A 1/3
6.1.3.2.2.
Radioactive
disintegration obeys N = N0 e-lt thus N/N0 =1/2 = e-lT1/2
6.1.3.2.3.
Taking
ln of both sides we get ln
½ = ln (-lT1/2 ) thus T1/2 = ln2/ l thus relating l to
T1/2
6.1.3.3.
Advanced
6.1.3.3.1.
Radioactive
decay obeys: dN(t) = -l N0 dt with the solution: N = N0 e-lt