Write the expression for the radius of `n^(th)` orbit of the hydrogenic atoms and give the meanings of the symbols used.

Explanation

Kinetic energy for the electron
`E_(k)=(1)/(2)mv^(2)`
But `(mv^(2))/( r)=(1)/(4pi epsi_(0).(Ze^(2))/(r^(2))`
`E_(k)=(1)/(2)((1)/(4pi epsi_(0)).(Ze^(2))/ (r ))=(1)/(8pi epsi_(0)).(Ze^(2))/( r )`
Potential energy, E = Charge `E_(p)`= Charge `xx` potential
`=-exx(1)/(4pi epsi_(0)).(Ze)/(r)=-(1)/(4pi epsi_(0)).(Ze^(2))/(r)`
Total energy `E=E_(k)+E_(p)`
`=(1)/(8pi epsi_(0)).(Ze^(2))/(r)-(1)/(4pi epsi_(0)).(Ze^(2))/( r )=-(1)/(8pi epsi_(0)).(Ze^(2))/( r )`
But radius `r=(epi_(0)n^(2)h^(2))/(nmZe^(2))`
substituting the value the value of r, we get
Total energy `T.E.=(-mZ^(2)e^(4))/(8 epsi_(0)^(2)n^(2)h^(2))`