Question

Which state of triply ionised beryllium (Be​​​​​3+)has the same orbital radius as that of the ground state of H-atom ?

Answer 1

Radius of electron in hydrogen atom = a0 n^2

where a0 is 52.9 pm
For ground state n = 1
thus radius of ground state = a0 ... eq 1

And radius of hydrogen like species is given by :
radius of electron in hydrogen like atom = a0 (n^2/z)
where Z is the atomic number of atom.

For Be3+ ion, Z = 4
Radius of electron in nth orbit of Be3+ ion = a0 (n^2/4) .. eq 2

Equating equation 1 and 2 to find the value of n

a0 (n^2/4) = a0
⇒n = 2

Thus 2nd state of the triply ionised beryllium(Be3+ ion) has the same orbit radius as that of ground state of hydrogen atom.