Formula for orbit radius: The radius of the nth orbit in a hydrogen-like ion is: rn=‌
n2a0
Z
Here, rn is the radius of the orbit, n is the orbit number, a0 is the Bohr radius, and Z is the atomic number. Radius for Hydrogen atom ( Z=1 ): For the second orbit of hydrogen ( n=2 ): rH=‌
22a0
1
=4a0 Radius for other ion: For an ion x with atomic number Z and orbit number n : rx=‌
n2a0
Z
Set radii equal to each other: Since the radii are equal: ‌
n2a0
Z
=4a0 Solve for n2 : Divide both sides by a0 : ‌
n2
Z
=4 Multiply both sides by Z : n2=4Z Find values for n and Z : Try Z=4 (which is for Be3+ ): n2=4×4=16 So, n=4. Answer: The orbit number n is 4 , and the ion x is Be3+.