a negative sign for all possible orbits (eq. . ). What does this negative sign convey?
This negative sign means that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest is an electron that is infinitely far away from the nucleus and is assigned the energy value of zero. Mathematically, this corresponds to setting n equal to infinity in the equation ( . ) so that E ∞ = .
As the electron gets closer to the nucleus (as n decreases), E n becomes larger in absolute value and more and more negative. The most negative energy value is given by n = which corresponds to the most stable orbit. We call this the ground state. Niels Bohr ( – ) Niels Bohr, a Danish physicist received his Ph.D.
from the University of Copenhagen in . He then spent a year with J.J. Thomson and Ernest Rutherford in England. In , he returned to Copenhagen where he remained for the rest of his life.
In he was named Director of the Institute of theoretical Physics. After first World War, Bohr worked energetically for peaceful uses of atomic energy. He received the first Atoms for Peace award in . Bohr was awarded the Nobel Prize in Physics in .
for the presence of negative sign in equation ( . ) and depicts its stability relative to the reference state of zero energy and n = ∞ . d) Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom. For example, He + Li + , Be + and so on.
The energies of the stationary states associated with these kinds of ions (also known as hydrogen like species) are given by the expression. E Z J . ( . ) and radii by the expression r pm n = .
( ) Z ( . ) where Z is the atomic number and has values , for the helium and lithium atoms respectively.