Download Atomic Structure and Radioactivity

Lecture 26
Atomic Structure and
Radioactivity
Chapter 29.1  29.4
Outline
• Properties of the Atomic Nucleus
• Binding Energy
• Radioactivity and Radioactive Decay
Nuclear Structure
The nucleus contains protons and neutrons,
collectively called nucleons.
Atoms of different chemical elements have
different number of protons (atomic number)
Atoms with the same number of protons and
different number of neutrons are called isotopes
A nucleus with a particular composition is called a
nuclide.
1 H – hydrogen atom with 1 proton in the nucleus
1
Atomic Structure
Size of the Nucleus
The nucleus size was found by E. Rutherford in
particle scattering experiments.
In head-on collisions, the entire kinetic energy is
converted to electrical potential energy at the
particle stopping point.
particle charge
1
q1q2
(2e) (Ze)
Target nucleus:
mv2 = ke = ke 
charge
2
r
r
size
2
4keZe
A  number of nucleons
r =  r = r0 A1/3
r0 = 1.2 1015 cm
mv2
Radioactivity
Radioactivity was discovered accidentally in 1896.
Henri Becquerel found that uranium (U) exposed a
photographic plate.
In other words, uranium emitted penetrating radiation.
Marie and Pierre Curie soon discovered 2 more
radioactive elements, called polonium and radium.
Radioactivity is associated with the nucleus and is
not affected by chemical reactions or heating.
Radioactive Decay
It was found that magnetic field splits the
radiation from radioactive materials into 3 parts.
Alpha () particles  positively charged
Beta () particles  negatively charged  electrons
Gamma () particles (rays)  no charge
- decay: the nucleus composition does not change.
-decay occurs in large, unstable, nuclei.
The heaviest stable isotope is 20983Bi.
-decay transforms a neutron into a proton (n  p+
+ e )
Electron capture: p+ + e  n and p+  n + e+
Half-Life
The half-life of a radionuclide is the period of time
needed for half of any its initial amount to decay.
1 mg 22688Ra  0.5 mg 22286Rn for 1600 years
Radionuclides have unchanging half-life.
This is the base for archaeological dating.
Half-life for 14C is 5730 years.
Radiation from radionuclides carries high energy.
It is harmful for living tissues.
1 sievert (Sv)  1 J of radiation from X-rays or rays absorbed by 1 kg of body tissue.
A permissible limit is ~ 20mSv a year.
Half-Life
The Decay Constant
N/t  N(t)
N = Nt

N(t) = N0 e t
N0/2 = N0 e T1/2

T1/2 = 0.693/
N  number of radionuclides
at some moment of time t
N  number of nuclei that
decay in a time interval t
  decay constant
N0  initial number of nuclei
T1/2  half-life
e = 2.718
Nuclear Energy
Our everyday life units for energy and mass are
not suitable for atoms.
The atomic mass unit (unified mass unit):
1u = 1.66 1027 kg
Mass of a hydrogen atom is 1.0078 u
The energy unit is the electronvolt (eV).
1eV = 1.60 1019 J
1Mev = 1.60 1013 J
E (1 u) = mc2 = 931 MeV
Binding Energy
Hydrogen has 3 isotopes: protium, deuterium, and
tritium.
The mass of 11H is 1.0078 u , the mass of a neutron
is 1.0087 u . The sum is 2.0165 u .
The mass of a deuterium atom is 2.0141 u: 0.0024 u
= 2.2 MeV less than the combined mass of p+n.
All atoms have smaller masses than the sum of masses
of their nucleons.
Some mass and energy is given off due to action of
forces that hold the protons and neutrons together.
This energy is called binding energy.
Binding Energy
Binding energy of a deuterium atom is 2.2 MeV
(1.1 MeV per nucleon) ,
of a 20983Bi is 1640 MeV (7.8 MeV per nucleon).
A typical binding energy is ~800 billion kJ/kg
To boil water it takes 2260 kJ/kg
The most stable element is iron (5626Fe).
Summary
Atomic nuclei consist of protons and neutrons.
Large nuclei are unstable and radioactively decay.
Radiation released by this process is dangerous
for living creatures.
The binding energy curve allows for two types of
nuclear reactions: fusion of light elements and
fission of heavy elements.