find kinetic energy, electrostatic potential energy and total
. energy of single electron in 2nd excited state of `Li^(+2)` atom.

Explanation

To find the kinetic energy, electrostatic potential energy, and total energy of a single electron in the second excited state of the `Li^(+2)` atom, we can follow these steps:

### Step 1: Identify the quantum numbers
The second excited state corresponds to the principal quantum number \( n = 3 \). For lithium, the atomic number \( Z = 3 \).

### Step 2: Calculate the total energy
The formula for the energy of an electron in a hydrogen-like atom is given by:

\[ E = -\frac{13.6 Z^2}{n^2} \]

Substituting the values for lithium:

\[ E = -\frac{13.6 \times 3^2}{3^2} \]

Calculating this gives:

\[ E = -\frac{13.6 \times 9}{9} = -13.6 \text{ eV} \]

### Step 3: Calculate the kinetic energy
The kinetic energy \( K \) of the electron in a hydrogen-like atom is equal to the absolute value of the total energy:

\[ K = |E| = 13.6 \text{ eV} \]

### Step 4: Calculate the electrostatic potential energy
The electrostatic potential energy \( U \) is given by:

\[ U = 2E \]

Substituting the value of \( E \):

\[ U = 2 \times (-13.6) = -27.2 \text{ eV} \]

### Step 5: Calculate the total energy
The total energy \( E_{total} \) is simply the sum of kinetic energy and potential energy:

\[ E_{total} = K + U \]

Substituting the values:

\[ E_{total} = 13.6 + (-27.2) = -13.6 \text{ eV} \]

### Summary of Results
- Kinetic Energy \( K = 13.6 \text{ eV} \)
- Electrostatic Potential Energy \( U = -27.2 \text{ eV} \)
- Total Energy \( E_{total} = -13.6 \text{ eV} \)