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 called 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.(19 th 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 % 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.

10 kilometers Nucleus 1 meter in size Mass of the atom Contains protons and neutrons Electrons Atom Mostly empty space ! Electric Force True size : 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 uncharged Atomic mass 7 Atomic charge 3 Four neutrons and three protons True size: m Neutrons and protons move around in the nucleus

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. Hydrogen – 1 proton Deuterium –1 proton and 1 neutron Tritium -- 1 proton and 2 neutrons. Tritium is radioactive with a half life of 12 years ! Tritium is three times more massive than hydrogen. H 1 1 H =DD H =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 nuclei with different nuclei with different numbers of protons and neutrons. N, Z N1 Z1 N2 Z2 + neutrons A = N+Z A1 =N1+Z1 A2=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 inches the fission process can run away and in a millionth of a second and release enormous amount of energy – an atom bomb will result. This is the critical mass of Uranium 235 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. Controls rods are devices made up of a substance which absorbs Slow neutrons and remove them from the chain reaction.

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.