An element with atomic number 64 will have the electronic configuration

Options

A. `[Xe]6s^2 4f^8`
B. `[Xe]6s^2 4f^7 5d^1`
C. `[Xe]4f^(10)`
D. `[Xe]6s^2 4f^7 5p^1`

Answer

To determine the electronic configuration of an element with atomic number 64, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number**: The atomic number (Z) of the element is given as 64. This means that in a neutral atom, there are 64 electrons.

2. **Understand the Order of Filling Orbitals**: Electrons fill orbitals in a specific order based on their energy levels. The order is generally:
- 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

3. **Fill the Orbitals According to the Order**:
- Start filling the orbitals with the maximum capacity:
- 1s² (2 electrons)
- 2s² (2 electrons)
- 2p⁶ (6 electrons)
- 3s² (2 electrons)
- 3p⁶ (6 electrons)
- 4s² (2 electrons)
- 3d¹⁰ (10 electrons)
- 4p⁶ (6 electrons)
- 5s² (2 electrons)
- 4d¹⁰ (10 electrons)
- 5p⁶ (6 electrons)
- 6s² (2 electrons)
- 4f⁷ (7 electrons)
- 5d¹ (1 electron)

4. **Count the Total Electrons**:
- Adding these up:
- 2 (1s) + 2 (2s) + 6 (2p) + 2 (3s) + 6 (3p) + 2 (4s) + 10 (3d) + 6 (4p) + 2 (5s) + 10 (4d) + 6 (5p) + 2 (6s) + 7 (4f) + 1 (5d) = 64 electrons.

5. **Write the Final Electronic Configuration**:
- The electronic configuration for the element with atomic number 64 (which is Gadolinium) is:
- [Xe] 6s² 4f⁷ 5d¹.

### Final Answer:
The electronic configuration of the element with atomic number 64 is:
**[Xe] 6s² 4f⁷ 5d¹**.