Will there the regular variations in the energy associated with successive principal quantum numbers of hydrogen-like atoms?

Explanation

No the variation will not be regular because, energy associated with an electron in n-th orbit, `E_(n)=(-2pi^(2)mZ^(2)e^(4))/(n^(2)h^(2))`
For a hydrogen-like atom, `(-2pi^(2)mZ^(2)e^(4))/(n^(2)h^(2))=`constant
`therefore E_(n)=(K)/(n^(2))" "`[K=constant]
`therefore E_(1)=(K)/(1^(2)),E_(2)=(K)/(2^(2)),E_(3)=(K)/(3^(2)),E_(4)=(K)/(4^(2)),` . . . etc.
From the values of the energy associated with the electrons, it is clear that the variation of energy in successive principal quantum number of hydrogen-like atoms, is not regular, in fact, the spacing between the energy levels decreases, as we move outwards from the nucleus.