Consider the hydrogen atom to be a proton embededded in a cavity of radius (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in a vacuum initially slowly .Estimate the average total energy of an electron in to ground state .Also if the magnitude of the average kinetic energy is half of the magnitude of the average energy ,find the average potential energy

Explanation

Coulombic force of attraction = Centrifugal force
`1/(4piE_(0))xx(Ze^(2))/(a_(0)^(2))=(mv^(2))/(a_(0))`
Where v= Volocity of electron
`a_(0)=` distance between electron and nucleus.
`1/(4pi E_(0))=(Ze^(2))/(a_(0))=mv^(2)`
`KE=1/2 mv^(2)=1/(4piE_(0)) . (Ze^(2))/(2a_(0))`
`PE=-2KE`