Answer:

Introduction:
Hydrogen atom and Helium ion are two chemical species. An electron is present in n1 orbit of hydrogen atom and n2 orbit of Helium ion. We have to find the correct relation for the same value of potential energy of electron in both the chemical species.

Potential Energy of Electron:
The potential energy of the electron in an orbital is given by the formula:

E = - (2.18 x 10^-18 J) (Z^2 / n^2)

Where E is the potential energy of the electron, Z is the atomic number of the element, and n is the principal quantum number of the electron.

Relation between Potential Energy and Principal Quantum Number:
The potential energy of an electron is directly proportional to the square of the principal quantum number. This means that if the principal quantum number of an electron is doubled, its potential energy will increase by a factor of four.

Relation between Potential Energy and Atomic Number:
The potential energy of an electron is inversely proportional to the square of the atomic number. This means that if the atomic number of an element is doubled, the potential energy of its electrons will decrease by a factor of four.

Relation between Potential Energy and Orbit:
The potential energy of an electron is inversely proportional to the square of the orbit radius. This means that if the radius of an orbit is doubled, the potential energy of the electron will decrease by a factor of four.

Conclusion:
From the above relations, we can conclude that for the same value of potential energy of electron in both the chemical species, the product of the square of the principal quantum number and the square of the atomic number should be the same. Therefore, we can write the following relation:

n1^2 Z1^2 = n2^2 Z2^2

Where n1 and Z1 are the principal quantum number and atomic number of hydrogen atom, and n2 and Z2 are the principal quantum number and atomic number of Helium ion.