Are the differences in energy between successive energy levels of a hydrogen-like atom same ? Explalin.

Explanation

No, the differences are not the same. Energy of an electron revolving in 'n' the orbit, `E_(n)=(2pi^(2)mz^(2)e^(4))/(n^(2)h^(2))`
Hence, the difference in energy betweenn first (n=1) and second (n=2) shell,
`E_(1)-E_(2)=-(2pi^(2)mz^(2)e^(4))/(h^(2))((1)/(1^(2))-(1)/(2^(2)))=-(2pi^(2)mz^(2)e^(4))/(h^(2))xx(3)/4`
Similarly, `E_(2)-E_(3)=-(2pi^(2)mz^(2)e^(4))/(h^(2))((1)/(2^(2))-(1)/(3^(2)))`
`=-(2pi^(2)mz^(2)e^(4))/(h^(2))xx(5)/(36)`
Obviously, `E_(1)-E_(2)neE_(2) -E_(3)`.