Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Coulomb's law as usual. Under such circumstances, calculate the ground state energy of a He-atom.

Explanation

As per the assumption made in the statement, since He atom also behaves like H-atom, we can apply Bohr.s atomic model to He atom. Hence
`E_(n)=(mZ^(2)e^(4))/(8 epsi_(0)^(2)n^(2)h^(2))`
`:.E_(n)=-(Z^(2))/(n^(2))((me^(4))/(8 epsi_(0)^(2)h^(2)))`
`:. E_(n)=-13.6 (Z^(2))/(n^(2))eV ( :. (me^(4))/(8 epsi_(0)^(2)h^(2))=13.6eV)`
Taking Z = 2 for He atom and n = 1 for groun state,
`E_(1)=-13.6xx((2)^(2))/((1)^(2))`
`:.E_(1)=-54.4eV`