Derive an expression for the potential energy and kinetic energy of an electron in any orbit of a hydrogen atom, according to Bohr's atomic model. How does P.E. change with increasing n?

Explanation

1) According to Bohr electrostatic force of attraction, `F_(e)` between the revolving electrons and nucleus provides the necessary centrietal force `F_(c)` to keep them in their orbits.
2) Thus for dynamically state orbit in a hydrogen atom:
`F_(c)=F_(e)rArr(mv^(2))/(r)=(1)/(4piepsi_(0))(e^(2))/(r_(2))`
3) The relation between the orbit radius and the electron velocity is `r=(e^(2))/(4pi epsi_(0)(mv^(2)))`
4) The Kinetic energy (K) and electrostatic potential energy (v) of the electron in hydrogen atom are
`K=(1)/(2) mv^(2)=(e^(2))/(8 pi epsi_(0)r) and v=(-e^(2))/(4pi epsi_(0)r)`
5) The total energy E of the electron in a hydrogen atom is
`E=K+U=(e^(2))/(8piepsi_(0)r)-(e^(2))/(4pi epsi_(0)r)`
`therefore E=(-e^(2))/(8pi epsi_(0)r)`
6) With increase in 'n' potential energy (U) also increases.