To find the energy required to convert a helium atom (He) into an alpha particle (which is essentially a helium nucleus, He²⁺), we need to consider the energy required to remove both electrons from the helium atom.
### Step-by-Step Solution:
1. **Understanding the Problem**:
We need to convert a neutral helium atom (He) into an alpha particle (which is a He²⁺ ion). This involves removing both electrons from the helium atom.
2. **Energy to Remove the First Electron**:
It is given that the energy required to remove one of the two electrons from a helium atom is \(29.5 \, \text{eV}\). This means that to remove the first electron, we need \(29.5 \, \text{eV}\).
3. **Energy to Remove the Second Electron**:
After removing the first electron, we have a He⁺ ion (which has one electron left). The remaining electron is in a hydrogen-like atom situation. The energy required to remove the second electron can be calculated using the formula for the energy levels of hydrogen-like atoms:
\[
E_n = -\frac{Z^2 \cdot E_0}{n^2}
\]
where \(Z\) is the atomic number (for helium, \(Z = 2\)), \(E_0 = 13.6 \, \text{eV}\), and \(n\) is the principal quantum number (for the first orbit, \(n = 1\)).
For He⁺, the energy required to remove the second electron is:
\[
E = -\frac{2^2 \cdot 13.6}{1^2} = -\frac{4 \cdot 13.6}{1} = -54.4 \, \text{eV}
\]
Since we are removing the electron, we take the positive value, so it is \(54.4 \, \text{eV}\).
4. **Total Energy Required**:
To find the total energy required to convert the helium atom into an alpha particle, we add the energy required to remove both electrons:
\[
\text{Total Energy} = \text{Energy to remove 1st electron} + \text{Energy to remove 2nd electron}
\]
\[
\text{Total Energy} = 29.5 \, \text{eV} + 54.4 \, \text{eV} = 83.9 \, \text{eV}
\]
5. **Conclusion**:
The energy required to convert a helium atom into an alpha particle is \(83.9 \, \text{eV}\).
### Final Answer:
The energy required to convert a helium atom into an alpha particle is \(83.9 \, \text{eV}\).
