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 areall hydrogen atoms wherever we find them the same andwhy are they stable.

It quantitatively explains the interaction of radiation andmatter.

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 regardedas complementary aspects of a single reality, like two sidesof a coin. According to quantum mechanics it is impossibleto measure both complementary quantities simultaneouslyto complete precision. If you know position exactly you cannot know its velocity.This is the essence of the Uncertainty Principle ofHeisenberg. Just as a tossed coin may fall either heads upor tails up, not both at once.Therefore it is impossible to know everything about a physical system. This shows up spectacularly when dealingwith microscopic objects – electron or photon.

Copenhagen Interpretation

As a physical system evolves in time it can lead to manydifferent outcomes. Quantum mechanics only predictsthe probabilities for all possible outcomes. Reality consistsof actual individual outcomes.

Bohr proposed that the act of observation turns the manypossibilities into a single actuality – a proposition that is calledthe 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 positivelycharged. 99.97 % of the mass of the atom is in theNucleus.

Atom is 10,000 bigger than the nucleus . Negativeelectrons move in this large volume and makethe atom as a whole electrically neutral.

10 kilometers

Nucleus1 meter in sizeMass of the atom Contains protonsand neutrons

Electrons

Atom Mostly emptyspace !

Electric Force

True size : 0.00000000005 m

Nucleus of the atom

Neutron

Proton

Element Lithium (used in batteries)

Held together by Strong nuclear force

Protons have positive electric charge

Neutrons are electrically unchargedAtomic mass 7

Atomic charge 3

Four neutrons and three protonsTrue size: 0.000000000000001 m

Neutrons and protons move around in the nucleus

Isotopes:

Different varieties of the same element for whichthe nucleus has the same number of protons butdifferent number of neutrons – so their masses aredifferent. Example: Hydrogen comes in three varieties, each having only one

proton.

Hydrogen – 1 proton Deuterium –1 proton and 1 neutronTritium -- 1 proton and 2 neutrons . Tritium is radioactive

with a half life of 12 years ! Tritium is three times more massive than hydrogen.

H1 1

H112 = DD

H113

=T

Isotopes Continued

The common isotope of Uranium has92 protons and 146 neutrons for

a total atomic mass of 238

A rare isotope of Uranium, importantin making a bomb or reactors has a massof 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 thenucleus together is the attractive nuclear force – a forcedifferent from the electric force and called the Strong force.

To break a nucleus one has to supply energy to overcomethe energy which binds it and keeps it together.

Similarly the atom itself is bound together by electricalforce 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 nuclei with different nuclei with different numbers of protonsand neutrons.

N, Z

N1Z1

N2Z2

+ neutrons

A = N+Z

A1 =N1+Z1

A2=N2+Z2

As protons and neutrons cannot be destroyedin fission

Number of Protons of the fissioning nucleus mustequal the number of protons of the fission productnuclei together. Z =Z1+Z2.

However the number of neutrons of the fissioningnucles equals the number of neutrons in productnuclei 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 inchesthe fission process can run away and in a millionth of a second and releaseenormous amount of energy – an atom bomb will result. This isthe critical mass of Uranium 235

If control rods are not operative in a reactor, the energy release canbe 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.

Controls rods are devices made up of a substance which absorbsSlow neutrons and remove them from the chain reaction.

Radioactivity is the spontaneous emission of different kinds of radiation from the nucleusof an atom.

Three kinds of radiation can be emitted:

1.Electrons or positrons called beta-rays2. Alpha particles which are nuclei of helium atoms3. Gamma radiation which is more energetic than X-rays.

It is gamma radiation which is most lethal radiationin bomb explosions.

Cyclotron

Cyclotron is a particle accelerator which producesvery energetic protons or similar nuclei. (Inventedby Ernest O. Lawrence of Berkeley in 1930s)

In Copenhagen, at Bohr's institute there was such a cyclotron, while there were no such machines inGermany at the time of World War II.

German physicists wanted to use this machine instudying processes which might help in making anatom bomb or a reactor.