The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?

Explanation

According to hypothesis of Bohr model.
`mvr=(nh)/(2pi)`
and centripetal force = coulomb force.
`(mv^(2))/(r)=(e^(2))/(4p epsi_(0)r^(2)) [ :.` For H, Z=1]
`:.(1)/(2) mv^(2)= (e^(2))/(8 pi epsi_(0)r)`
`:.k=(e^(2))/(8 pi epsi_(0)r)`
`:. K=(e^(2))/(8 pi epsi_(0)r )" "...(1)`
and potential energy ,
`U=-(e-e)/(4pi epsi_(0)r)=(-e^(2))/(4pi epsi_(0)r) " "...(2)`
`:.U=-((e^(2))/(8 pi epsi_(0)r))=-2K" "...(3) `
and E=K+U
`=K+(-2k)`
`:.E=-K " "..(4)`
If we select the value of potential energy zero by other way then the kinetic energy does not change. Hence, the value of kinetic energy is + 3.4 eV, which is independent of the zero of the potential energy. If the value of the potential energy taken zero, then the potential energy of and total energy of that state will change.