What is Quantum Mechanics ?
Quantum Mechanics describes the laws that govern the
time evolution and the behaviour of any physical system.
They are the laws of motion and incorporate the
principles of relativity.
It explains the stability and identity of atoms – why are
all hydrogen atoms wherever we find them the same and
why are they stable.
It quantitatively explains the interaction of radiation and
matter.
The Bohr Complementarity Principle
To describe the motion of an object, at each instant of
time one must have complete knowledge of its
position and its velocity – two “ complementary” quantities.
The wave and particle properties of object can be regarded
as complementary aspects of a single reality, like two sides
of a coin. According to quantum mechanics it is impossible
to measure both complementary quantities simultaneously
to complete precision. If you know position exactly you
cannot know its velocity.
This is the essence of the Uncertainty Principle of
Heisenberg. Just as a tossed coin may fall either heads up
or tails up, not both at once.
Therefore it is impossible to know everything about a
physical system. This shows up spectacularly when dealing
with microscopic objects – electron or photon.
Copenhagen Interpretation
As a physical system evolves in time it can lead to many
different outcomes. Quantum mechanics only predicts
the probabilities for all possible outcomes. Reality consists
of actual individual outcomes.
Bohr proposed that the act of observation turns the many
possibilities into a single actuality – a proposition that is call
the Copenhagen interpretation. By repeatedly doing the
experiment one can determine the quantum mechanical
probabilities. According to Bohr this is the only meaningful
interpretation.
The Nucleus
Matter is made up of atoms.(19th century)
Whole atoms are electrically neutral.
Atoms have structure – shown by Rutherford(1911):
Most of the mass of the atom is concentrated in
a small volume – called the nucleus. It is positively
charged. 99.97 % of the mass of the atom is in the
Nucleus.
Atom is 10,000 bigger than the nucleus . Negative
electrons move in this large volume and make
the atom as a whole electrically neutral.
Atom
Mostly empty
space !
Electrons
Electric Force
10 kilometers
Nucleus
1 meter in size
Mass of the atom
Contains protons
and neutrons
True size : 0.00000000005 m
Nucleus of the atom
Element Lithium (used in batteries)
Four neutrons and three protons
True size: 0.000000000000001 m
Neutron
Proton
Atomic mass 7
Atomic charge 3
Protons have positive
electric charge
Neutrons are
electrically
uncharged
Neutrons and protons
move around in the nucleus
Held together by Strong nuclear force
Isotopes:
Different varieties of the same element for which
the nucleus has the same number of protons but
different number of neutrons – so their masses are
different.
Example: Hydrogen comes in three varieties, each having only one
proton.
1
Hydrogen – 1 proton1H
2H
Deuterium –1 proton and 1 neutron1 = DD
1
Tritium -- 1 proton and 2 neutrons . Tritium is radioactive
with a half life of 12 years ! 3
Tritium is three times more massive than hydrogen.
11H =T
Isotopes Continued
The common isotope of Uranium has
92 protons and 146 neutrons for
a total atomic mass of 238
A rare isotope of Uranium, important
in making a bomb or reactors has a mass
of 235 – consisting of 92 protons and
143 neutrons.
Why does the nucleus not fly apart ?
Like charges repel each other, hence the protons try to
fly away from each other in the nucleus. What keeps the
nucleus together is the attractive nuclear force – a force
different from the electric force and called the Strong force.
To break a nucleus one has to supply energy to overcome
the energy which binds it and keeps it together.
Similarly the atom itself is bound together by electrical
force between the protons and the surrounding electrons.
Energy usually has to be supplied to break up atoms.
Fission
The process by which a nucleus with a given number of
protons(Z) and neutrons(N) can split up into two other nucle
with different nuclei with different numbers of protons
and neutrons.
A1 =N1+Z1
N1
Z1
N, Z
A = N+Z
+ neutrons
A2=N2+Z2
N2
Z2
As protons and neutrons cannot be destroyed
in fission
Number of Protons of the fissioning nucleus must
equal the number of protons of the fission product
nuclei together. Z =Z1+Z2.
However the number of neutrons of the fissioning
nucles equals the number of neutrons in product
nuclei plus the number of neutrons released in a
fission.
N = N1 + N2 + number of neutrons emitted
There are two kinds of fission processes:
1. Spontaneous fission where the nucleus by
itself fissions, without external excitation.
2. Induced fission, caused by the absorption
of a neutron by a nucleus which then
undergoes fission. Uranium 235 can easily
capture a slow neutron and undergo fission
and in turn releases 2 or more neutrons
making it possible to sustain a chain reaction.
Hence it is important for generating power
or making an explosion.
Neutron Induced fission of Uranium 235
Chain Reaction with Uranium 235
Fission products Krypton and Barium – radioactive
Critical Mass
If you can pack 24 pounds of Uranium235 in a sphere of radius 3.4 inche
the fission process can run away and in a millionth of a second and relea
enormous amount of energy – an atom bomb will result. This is
the critical mass of Uranium 235
Controls rods are devices made up of a substance which absorbs
Slow neutrons and remove them from the chain reaction.
If control rods are not operative in a reactor, the energy release can
be exponentially large and the reactor can have a meltdown !
In Copenhagen, Bohr asks Heisenberg about use of control
rods in a reactor – a point Heisenberg did not seem to be aware of.
Radioactivity is the spontaneous emission of
different kinds of radiation from the nucleus
of an atom.
Three kinds of radiation can be emitted:
1.Electrons or positrons called beta-rays
2. Alpha particles which are nuclei of helium atoms
3. Gamma radiation which is more energetic than
X-rays.
It is gamma radiation which is most lethal radiation
in bomb explosions.
Cyclotron
Cyclotron is a particle accelerator which produces
very energetic protons or similar nuclei. (Invented
by Ernest O. Lawrence of Berkeley in 1930s)
In Copenhagen, at Bohr's institute there was such
a cyclotron, while there were no such machines in
Germany at the time of World War II.
German physicists wanted to use this machine in
studying processes which might help in making an
atom bomb or a reactor.