The hydrogen -like species `Li^(2+)` is in a spherically symmetric state `S_(1)` with one node. Upon absorbing light , the ion undergoes transition to a state `S_(2)`. The state `S_(2)` has one radial node and its energy is equal is to the ground state energy of the hydrogen atom.
Energy of the state `S_(1)` in units of the hydrogen atom ground state energy is

Options

A. `0.75`
B. `1.50`
C. `2.25`
D. `4.50`

Explanation

To solve the problem, we need to determine the energy of the state \( S_1 \) in units of the ground state energy of the hydrogen atom. Let's break it down step by step.

### Step 1: Identify the state \( S_1 \)
The state \( S_1 \) is described as being spherically symmetric with one node. For hydrogen-like atoms, the number of nodes in an orbital is given by the formula:
\[ \text{Number of nodes} = n - 1 \]
where \( n \) is the principal quantum number. Since \( S_1 \) has one node, we can set up the equation:
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