Consider a system containing a negatively charge poin `(pi, m_(pi) = 273^(@)m_(e))` orbital around a staionary nucleus of atomic number Z .The total energy `(E_(n))` of ion is half of its potential energy `(PE_(n))` in nth sationary state .The motion of the poin can be assumed to be in a uniform circular notion with centripents force given by the force of attaraction between the positive uncless and the point .Assume that point revolves only in the stationary satte defined by the quantisation of its angular momentum about the nucless as Bohr's model
The potential energy `(PE_(n))` of ion follows:

Options

A. `PE_(n) prop m_(pi) ((n^(2))/(Z))`
B. `PE_(n) prop m_(pi) ((Z^(2))/(n^(2)))`
C. `PE_(n) prop (1)/(m_(pi)) ((n^(2))/(Z^(2)))`
D. `PE_(n) prop (1)/(m_(pi)) ((Z^(2))/(n^(2)))`

Answer

B

Explanation

`PE_(n) (magnitude) prop m_(n)- (Z^(2))/(n^(2)) (= 2E_(n))`