Supposing the electron of the hydrogn atom is present in the L- shell if it liberates 10.2 eV what is the energy of the system ?

Options

A. `-3.4 eV`
B. `-13.6 eV`
C. `-10.2 eV`
D. 0 eV

Answer

To solve the problem, we need to determine the energy of the hydrogen atom's electron when it is in the L shell and how the liberation of energy affects the overall energy of the system.

### Step-by-Step Solution:

**Step 1: Identify the Principal Quantum Number for the L Shell**
- The L shell corresponds to the principal quantum number \( n = 2 \).

**Step 2: Calculate the Energy of the Electron in the L Shell**
- The energy of an electron in a hydrogen atom at a given shell can be calculated using the formula:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]
- For the L shell (\( n = 2 \)):
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \]

**Step 3: Understand the Energy Liberation**
- The problem states that the electron liberates 10.2 eV of energy. This energy corresponds to the transition from the L shell to the K shell.

**Step 4: Calculate the Energy of the Electron in the K Shell**
- The K shell corresponds to \( n = 1 \):
\[ E_1 = -\frac{13.6 \text{ eV}}{1^2} = -13.6 \text{ eV} \]

**Step 5: Determine the Energy of the System After Liberation**
- The energy of the system after the electron transitions from the L shell to the K shell is simply the energy of the electron in the K shell:
\[ \text{Energy of the system} = E_1 = -13.6 \text{ eV} \]

### Final Answer:
The energy of the system after the electron liberates 10.2 eV and transitions to the K shell is **-13.6 eV**.

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