Question

Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the n^th orbit of an atom.

Answer 1

Let ‘e’, ‘m’, and ‘v’ be the charge, mass, and velocity of electrons, respectively, and ‘r’ is the radius of the orbit.

The positive charge on the nucleus is Ze, where Z is the atomic number (in case of hydrogen atom Z = 1).

As the electrostatic force of attraction provides the centripetal force.

`(mv^2)/r = 1/(4piepsilon_0) (("Ze") xx "e")/r^2`

`=> mv^2 = "Ze"^2/(4piepsilon_0r)`

`=> v = sqrt("Ze"^2/(4piepsilon_0" rm"))`