Identify Ground or Excited State S1 of Lithium Ion

To determine the state $\text{S}_1$ of the hydrogen-like species $\text{Li}^{2+}$, we analyze the given properties of $\text{S}_1$:

1. Spherically Symmetric State:
   A wave function is spherically symmetric if its angular part is independent of the angles $\theta$ and $\phi$. This property corresponds to an azimuthal quantum number of $l = 0$, which signifies an $\text{s}$-orbital.

2. Radial Nodes:
   The number of radial nodes for a hydrogen-like atomic orbital is given by the formula:
   $\text{Number of radial nodes} = n - l - 1$

   Given that state $\text{S}_1$ has $1$ radial node and $l = 0$:
   $1 = n - 0 - 1$
   $n = 2$

Thus, with principal quantum number $n = 2$ and azimuthal quantum number $l = 0$, the state $\text{S}_1$ corresponds to the $2\text{s}$ orbital.

Correct Option: B ($2\text{s}$)