Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [53]
Bohr had met Nicholson during his abortive stay in Cambridge, and had not been overly impressed. Only a few years older at 31, Nicholson had since been appointed professor of mathematics at King's College, University of London. He had also been busy building an atomic model of his own. He believed that the different elements were actually made up of various combinations of four 'primary atoms'. Each of these 'primary atoms' consisted of a nucleus surrounded by a different number of electrons that formed a rotating ring. Though, as Rutherford said, Nicholson had made an 'awful hash' of the atom, Bohr had found his second clue. It was the physical explanation of the stationary states, the reason why electrons could occupy only certain orbits around the nucleus.
An object moving in a straight line has momentum. It is nothing more than the object's mass times its velocity. An object moving in a circle possesses a property called 'angular momentum'. An electron moving in a circular orbit has an angular momentum, labelled L, that is just the mass of the electron multiplied by its velocity multiplied by the radius of its orbit, or simply L=mvr. There were no limits in classical physics on the angular momentum of an electron or any other object moving in a circle.
When Bohr read Nicholson's paper, he found his former Cambridge colleague arguing that the angular momentum of a ring of electrons could change only by multiples of h/2, where h is Planck's constant and (pi) is the well-known numerical constant from mathematics, 3.14….17 Nicholson showed that the angular momentum of a rotating electron ring could only be h/2 or 2(h/2) or 3(h/2) or 4(h/2) … all the way to n(h/2) where n is an integer, a whole number. For Bohr it was the missing clue that underpinned his stationary states. Only those orbits were permitted in which the angular momentum of the electron was an integer n multiplied by h and then divided by 2. Letting n=1, 2, 3 and so on generated the stationary states of the atom in which an electron did not emit radiation and could therefore orbit the nucleus indefinitely. All other orbits, the non-stationary states, were forbidden. Inside an atom, angular momentum was quantised. It could only have the values L=nh/2 and no others.
Just as a person on a ladder can stand only on its steps and nowhere in between, because electron orbits are quantised, so are the energies that an electron can possess inside an atom. For hydrogen, Bohr was able to use classical physics to calculate its single electron's energy in each orbit. The set of allowed orbits and their associated electron energies are the quantum states of the atom, its energy levels En. The bottom rung of this atomic energy ladder is n=1, when the electron is in the first orbit, the lowest-energy quantum state. Bohr's model predicted that the lowest energy level, E1, called the 'ground state', for the hydrogen atom would be -13.6eV, where an electron volt (eV) is the unit of measurement adopted for energy on the atomic scale and the minus sign indicates that the electron is bound to the nucleus.18 If the electron occupies any other orbit but n=1, then the atom is said to be in an 'excited state'. Later called the principal quantum number, n is always an integer, a whole number, which designates the series of stationary states that an electron can occupy and the corresponding set of energy levels, En, of the atom.
Bohr calculated the values of the energy levels of the hydrogen atom and found that the energy of each level was equal to the energy of the ground state divided by n2, (E1/n2)eV. Thus, the energy value for n=2, the first excited state, is -13.6/4 = -3.40eV. The radius of the