The first ionization energy of hydrogen is `2.179xx10^(-18)` J
The second ionization energy of helium atom will be

Options

A. `8.716xx10^(-18)J`
B. `4.358xx10^(-18)J`
C. `5.45xx10^(-17)` J
D. `1.09xx10^(-18) J`

Explanation

To find the second ionization energy of a helium atom based on the first ionization energy of hydrogen, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between ionization energy and nuclear charge:**
According to Bohr's theory, the energy of an electron in an atom is given by the formula:
\[ E \propto \frac{Z^2}{n^2} \]
where \(E\) is the energy, \(Z\) is the nuclear charge, and \(n\) is the principal quantum number.

2. **Identify the values for hydrogen:**
For hydrogen (\(H\)):
- The nuclear charge \(Z = 1\)
- The principal quantum number \(n = 1\)
- The first ionization energy of hydrogen is given as:
\[ E_H = 2.179 \times 10^{-18} \text{ J} \]

3. **Calculate the first ionization energy for helium:**
For helium (\(He\)):
- The nuclear charge \(Z = 2\)
- The principal quantum number \(n = 1\)
- The energy for helium can be calculated using the relation:
\[ E_{He} \propto \frac{Z^2}{n^2} = \frac{2^2}{1^2} = 4 \]
Therefore, the ionization energy of helium is:
\[ E_{He} = 4 \times E_H = 4 \times (2.179 \times 10^{-18} \text{ J}) \]

4. **Perform the calculation:**
\[ E_{He} = 4 \times 2.179 \times 10^{-18} = 8.716 \times 10^{-18} \text{ J} \]

5. **Conclusion:**
The second ionization energy of helium is:
\[ E_{He} = 8.716 \times 10^{-18} \text{ J} \]

### Final Answer:
The second ionization energy of the helium atom is \(8.716 \times 10^{-18} \text{ J}\).

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