The energy of an electron in Bohr's orbit of hydrogen atom is `-13.6eV`. The total electronic energy of a hypothetical He atom in which there are no electron - electron repulsions or interactions is

Options

A. 27.2 eV
B. `-27.2 eV`
C. `-108.8 eV`
D. 108. eV

Answer

To find the total electronic energy of a hypothetical helium atom where there are no electron-electron repulsions or interactions, we can follow these steps:

### Step 1: Understand the Energy Formula
The energy of an electron in a Bohr orbit is given by the formula:
\[ E_n = -\frac{E_0 Z^2}{n^2} \]
where:
- \(E_0\) is the energy of the electron in the first orbit of hydrogen, which is \(-13.6 \, \text{eV}\),
- \(Z\) is the atomic number (2 for helium),
- \(n\) is the principal quantum number (1 for the first orbit).

### Step 2: Calculate the Energy for Helium
For helium, we substitute \(Z = 2\) and \(n = 1\) into the formula:
\[ E_1 = -\frac{E_0 \cdot Z^2}{n^2} = -\frac{-13.6 \cdot 2^2}{1^2} \]
Calculating this gives:
\[ E_1 = -\frac{-13.6 \cdot 4}{1} = -54.4 \, \text{eV} \]

### Step 3: Calculate Total Energy for Two Electrons
Since we have two electrons in helium, and assuming no electron-electron interactions, the total energy \(E_{\text{total}}\) will be the sum of the energies of both electrons:
\[ E_{\text{total}} = 2 \cdot E_1 = 2 \cdot (-54.4 \, \text{eV}) = -108.8 \, \text{eV} \]

### Final Answer
The total electronic energy of the hypothetical helium atom is:
\[ \boxed{-108.8 \, \text{eV}} \]