The energy of the electron in` Be^(3+)` ion depends on

Options

A. the principal quantum number only.
B. the principal and azimuthal quantum numbers only.
C. the principal, azimuthal and magnetic quantum numbers
D. the principal, azimuthal, magnetic and spin quantum numbers.

Explanation

To solve the question regarding the energy of the electron in the Be^(3+) ion, we will use the Bohr model of the atom. Let's break down the solution step by step.

### Step 1: Understand the Bohr Model Formula
The energy of an electron in a hydrogen-like atom can be calculated using the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where:
- \( E_n \) is the energy of the electron at the principal quantum number \( n \),
- \( Z \) is the atomic number of the element,
- \( n \) is the principal quantum number.

### Step 2: Identify the Atomic Number and Electron Configuration
For the Be^(3+) ion:
- The atomic number (Z) of beryllium (Be) is 4.
- The Be^(3+) ion means it has lost 3 electrons. Therefore, it has only 1 electron left, which is in the 1s orbital.

### Step 3: Determine the Values of Z and n
- For Be^(3+), the remaining electron is in the ground state, so:
- \( Z = 4 \) (for beryllium)
- \( n = 1 \) (since there is only one electron remaining)

### Step 4: Calculate the Energy
Using the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot 4^2}{1^2} \]
\[ E_n = -\frac{13.6 \, \text{eV} \cdot 16}{1} \]
\[ E_n = -217.6 \, \text{eV} \]

### Step 5: Analyze the Options
The energy of the electron in the Be^(3+) ion depends on:
- The principal quantum number \( n \)
- The atomic number \( Z \)

However, the question asks which of the following depends on the energy of the electron. The principal quantum number \( n \) is the only option that is mentioned in the choices provided.

### Conclusion
Thus, the energy of the electron in the Be^(3+) ion depends on the principal quantum number \( n \).

### Final Answer
The energy of the electron in Be^(3+) ion depends on the principal quantum number \( n \).

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