Use Bohr's formula to calculate the energy required to excite the electron from ground state to second level of helium (`He^+`) atom. Use Z = 2.

Answer

To calculate the energy required to excite the electron from the ground state to the second level of the helium ion (He⁺) using Bohr's formula, we will follow these steps:

### Step 1: Understand Bohr's Energy Formula
Bohr's formula for the energy levels of an electron in a hydrogen-like atom is given by:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
where:
- \(E_n\) is the energy of the electron at level \(n\),
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number.

### Step 2: Calculate the Energy for Ground State (n=1)
For the ground state of helium (He⁺), where \(Z = 2\) and \(n = 1\):
\[ E_1 = -\frac{13.6 \times 2^2}{1^2} = -\frac{13.6 \times 4}{1} = -54.4 \, \text{eV} \]

### Step 3: Calculate the Energy for Second Level (n=2)
Now, we calculate the energy for the second level of helium (He⁺), where \(Z = 2\) and \(n = 2\):
\[ E_2 = -\frac{13.6 \times 2^2}{2^2} = -\frac{13.6 \times 4}{4} = -13.6 \, \text{eV} \]

### Step 4: Calculate the Energy Required for Excitation
The energy required to excite the electron from the ground state to the second level is given by the difference in energy between these two states:
\[ \Delta E = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = -13.6 - (-54.4) = -13.6 + 54.4 = 40.8 \, \text{eV} \]

### Final Answer
The energy required to excite the electron from the ground state to the second level of the helium ion (He⁺) is:
\[ \Delta E = 40.8 \, \text{eV} \]

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