Question
Show that the radius of the orbit in hydrogen atom varies as , where n is the principal quantum number of the atom.
Solution
The electrostatic force of attraction between nucleus and the electron is,
According to Bohr’s theory, a hydrogen atom consists of a nucleus with a positive charge e and a single electron of charge –e, which revolves around it in circular orbit of radius r.
To keep electron bound to its orbit, centripetal force on the electron becomes equal to the electrostatic attraction. Therefore, 
where,
m is the mass of electron, and
v is the speed of an orbit of radius r.
Now, using Bohr’s quantisation condition for angular momentum,
where, n is the principal quantum number.
