Radius of the first excited state of Helium ion is given as : $$a_0\rightarrow$$ radius of first stationary state of hydrogen atom.

We need to find the radius of the first excited state of the Helium ion (He⁺).

The radius of the nth orbit for a hydrogen-like atom is:

$$r_n = \frac{n^2 a_0}{Z}$$

Here, $$a_0$$ is the Bohr radius (the radius of the first orbit of hydrogen) and Z is the atomic number.

For He⁺, Z = 2, and the first excited state corresponds to n = 2. Substituting these values gives

$$r = \frac{(2)^2 \times a_0}{2} = \frac{4a_0}{2} = 2a_0$$

The correct answer is Option 2: $$r = 2a_0$$.