If energy required to remove one of the two electrons from He atom is `29.5 eV`, then what is the value of energy required to convert a helium atom into `alpha`-particle?

Options

A. `54.4 eV`
B. `83.9 eV`
C. `29.5 eV`
D. `24.9 eV`

Answer

To solve the problem of finding the energy required to convert a helium atom into an alpha particle, we can follow these steps:

### Step 1: Understand the Components
We know that a helium atom (He) has two electrons and consists of two protons and two neutrons. An alpha particle is essentially the same as a helium nucleus (He²⁺), which means we need to remove both electrons from the helium atom.

### Step 2: Calculate the Energy to Remove Electrons
We are given that the energy required to remove one of the two electrons from a helium atom is 29.5 eV. Since we need to remove both electrons, we will multiply this energy by 2:

\[ \text{Energy to remove both electrons} = 2 \times 29.5 \, \text{eV} = 59.0 \, \text{eV} \]

### Step 3: Calculate the Binding Energy of the Helium Nucleus
Next, we need to find the binding energy of the helium nucleus. According to the Bohr model, the total energy of a hydrogen-like atom can be calculated using the formula:

\[ E = -\frac{Z^2 \cdot E_0}{n^2} \]

where:
- \( Z \) is the atomic number (for helium, \( Z = 2 \)),
- \( E_0 = 13.6 \, \text{eV} \) (the energy of the ground state of hydrogen),
- \( n \) is the principal quantum number (for the ground state, \( n = 1 \)).

Substituting the values:

\[ E = -\frac{2^2 \cdot 13.6 \, \text{eV}}{1^2} = -\frac{4 \cdot 13.6 \, \text{eV}}{1} = -54.4 \, \text{eV} \]

### Step 4: Calculate the Total Energy Required
To find the total energy required to convert the helium atom into an alpha particle, we need to add the energy required to remove the electrons and the binding energy of the helium nucleus:

\[ \text{Total Energy} = \text{Energy to remove electrons} + \text{Binding Energy} \]

Substituting the values:

\[ \text{Total Energy} = 59.0 \, \text{eV} + 54.4 \, \text{eV} = 113.4 \, \text{eV} \]

### Conclusion
The total energy required to convert a helium atom into an alpha particle is **113.4 eV**.

---