Nuclear forces and
Radioactivity
Two forces are at work inside the
nucleus of an atom
Forces act in opposing directions

Electrostatic repulsion: pushes protons apart



Strong nuclear force: pulls protons together



Nuclear force is much shorter range: protons must be close together
Neutrons only experience the strong
nuclear force

Proton pair experiences both forces




Neutrons experience only the strong nuclear force
But: neutrons alone are unstable
Neutrons act like nuclear glue

Helium nucleus contains 2 protons and 2
neutrons – increase attractive forces

Overall nucleus is stable




As nuclear size increases,
electrostatic repulsion builds up

There are electrostatic repulsions between
protons that don’t have attractive forces
Long range
repulsive force
with no
compensation
from attraction







More neutrons required
Neutron to proton ratio increases
with atomic number
Upper
limit of
stability
4
U  234
90Th  2 He
238
92
Upper limit to nuclear stability


Beyond atomic number 83, all nuclei are
unstable and decay via radioactivity
Radioactive decay (Transmutation) –
formation of new element
Mass
number
Atomic
number
U  Th He  
238
92
Atomic
number
decreases
234
90
4
2
Alpha
particle
emitted
Beta particle emission

Neutron is converted into a proton + electron


Proton stays in nucleus
Electron is emitted (beta particle)

0
1
e
Atomic number increases with beta
emission

Here atomic number actually increases, but
serves to reduce the neutron:proton ratio
Th Pa  e  
234
90


234
91
0
1
Beta particle emission occurs with neutron-excess nuclei
Alpha particle emission occurs with proton-heavy nuclei
Beta
particle
emitted
Positrons and antimatter

Protons are converted to neutron and positively
0
charged electron (positron)


Neutron stays in nucleus
Positron emitted
1
e


Positron is antimatter and is annihilated by
0
0
electron:
1 e 1 e  
Summary of nuclear processes

Alpha emission:


Beta emission:


Mass number same, atomic number increases
Positron emission:


Mass number and atomic number decrease
Mass number same, atomic number decreases
Gamma ray emission:

Mass number and atomic number same
Analyzing nuclei: filling in the
blanks



Mass number = protons + neutrons
Atomic number = protons
Element identity = atomic number
Writing nuclear equations

1.
2.
Rules for balancing nuclear equations:
Conserve mass number (protons + neutrons)
Conserve atomic number (nuclear charge)
Th Pa  ?
234
90
234
91
Th  ? e
234
90
0
1
Th Pa X
234
90



234
91
Mass number sum:
234 = 234 + ?
?=0
Atomic number sum:
90 = 91 + ?
? = -1
0
Particle is
e
1
?
?
Th X  e
234
90



?
?
Mass number sum:
234 = ? + 0
? = 234
Atomic number sum:
90 = ? - 1
? = 91
Nucleus is
234
91
Pa
0
1
Worked examples
226
88
Ra  ? He
4
2
Co  ? e
60
27
0
1
Creation of radioisotopes

Isotopes are created by bombarding nuclei
with smaller particles

Neutrons

Protons

Alpha particles 10 B  4He 13N  1n
98
42
66
30
Mo  n Mo
1
0
Zn H  Ga
1
1
5

Other nuclei
99
42
67
31
2
7
0
Cf  N  N  4 n
249
98
15
7
260
105
1
0
Radioactive decay occurs in series of
steps
The decay series from uranium-238 to lead-206. Each nuclide except for the
last is radioactive and undergoes nuclear decay. The left-pointing, longer
arrows (red) represent alpha emissions, and the right-pointing, shorter arrows
(blue) represent beta emissions.
Half-life measures rate of decay


Concentration of
nuclide is halved after
the same time interval
regardless of the initial
amount – Half-life
Can range from
fractions of a second to
millions of years
Half-life calculations


131I
decays to 131Xe with a half-life of 8 days
How much remains after 40 days if there are 10 grams
initially?
The Dating Game

Carbon-14 is produced in the upper atmosphere by the
bombardment of nitrogen atoms with neutrons:

14
N + 1 n  14 C + 1 H
7
0
6
1

Radioactive 14CO2 is produced, which mixes with ordinary 12CO2 and
is taken up by plants during photosynthesis.
Carbon Dating
• During an organism’s life,
14CO and 12CO are in
2
2
equilibrium at a ratio of 1:1012.
• When organism dies, 14C/12C
ratio decreases as 14C
undergoes b decay to 14N.
• Measuring 14C/12C ratio
determines age of sample with
high degree of certainty.
•
Ages of 1000–20,000 years
are commonly determined.
The half-life for 14C is 5730
years.
The age of the earth





U-238 decays eventually to Pb-206
Since half-life of U-238 is so long (4.5 billion years),
the atom of Pb-206 appears almost instantly after its
decay
If the mineral was once pure U-238, after some
billions of years it becomes a mixture of U and Pb
Measuring the ratio of Pb:U gives us the age of the
rock
Note that the U-238 half-life is of the order of the age
of the earth. If the earth was 6,000 years old or 50
billion years old it would not work
Other nuclear processes:
fission and fusion

Attempts to grow larger
nuclei by bombardment
with neutrons yielded
smaller atoms instead.


Distorting the nucleus causes the
repulsive forces to overwhelm the
attractive
The foundation of
nuclear energy and the
atomic bomb
Inter-changeability of mass and
energy

When a radioactive nucleus divides to give two smaller ones,
the combined mass of them is lower
AB+C

MA > MB + MC
Loss in mass equals energy given out
E = mc2

Tiny amount of matter produces masses of energy:
1 gram  1014 J
In chemical process 1 gram may produce 103 J (1011 less)

Energy and mass are conserved, but can be inter-changed

Nuclear fission

Nuclear fission produces nuclei with lower
nucleon mass
1
0

n
U  Kr  Ba 3 n
235
92
91
36
142
56
1
0
One neutron produces three: the basis for a
chain reaction – explosive potential
Chain reactions require rapid multiplication
of species
Nuclear fusion


Small nuclei fuse to yield larger ones – losing
nucleon mass
+E
Example is the deuterium – tritium reaction



High energy output
Clean products – no long-lived radioactive waste or toxic heavy metals
Problem is providing enough energy to initiate
the process
Biological Effects of Radiation

The penetrating power of radiation is a function of its
mass: -rays > b-particles >> -particles.

When ionizing radiation passes through tissue it
removes an electron from water to form H2O+ ions.

The H2O+ ions react with another water molecule to
produce H3O+ and a highly reactive •OH radical.

Free radicals generally undergo chain reactions,
producing many radicals in the biomolecules.
Biological Effects of Radiation 02

-rays are particularly
harmful because they
penetrate in the same way as
X rays.

-particles interact with the
skin and b-particles interact
up to 1 cm into the tissue

-particles are particularly
dangerous when ingested or
inhaled.
Different units for measuring
radiation
The Curie
Measure of amount of
radioactivity
The Roentgen (gamma and Xray)
Measure of interaction with air
The Rad
Radiation absorbed dose
Amount of material that
produces 3.7x1010 decays per
second
The Rem
Measure of biological damage
Determined from rem and some
factor which depends on the
type radiation (1 for beta and 10
for alpha)
Amount of radiation needed to
produce 2x1010 ion pairs in air
Dosage of radiation able to
transfer 2.4x10-3 cal to one kg
of matter
Biological Effects of Radiation




Not all forms of radiation have the same efficiency
for biological damage.
To correct, the radiation dose is multiplied by the
relative biological effectiveness (RBE), which gives
the roentgen equivalent for man (rem).
RBE is about 1 for b- and - and 10 for  radiation.
SI unit for effective dosage is the Sievert
(1 Sv = RBE x 1 Gy = 100 rem).
Biological Effects of Radiation
Sources of radiation