The electronic configuration of gadolinium (Atomic number 64) is

Options

A. [Xe] `4f^(3) 5d^(5) 6s^(2)`
B. `[Xe] 4f^(7) 5d^(2) 6s^(1)`
C. [Xe] `4f^(7) 5d^(1) 6s^(2)`
D. [Xe] `4f^(8) 5d^(6) 6s^(2)`

Explanation

To determine the electronic configuration of gadolinium (atomic number 64), we can follow these steps:

### Step 1: Identify the Element and its Atomic Number
Gadolinium has an atomic number of 64. This means it has 64 electrons.

### Step 2: Understand the Electron Filling Order
Electrons fill atomic orbitals according to the Aufbau principle, which states that electrons occupy the lowest energy orbitals first. The order of filling is as follows:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, etc.

### Step 3: Fill the Orbitals up to Atomic Number 64
1. Start filling from 1s up to 6s:
- 1s² (2)
- 2s² (4)
- 2p⁶ (10)
- 3s² (12)
- 3p⁶ (18)
- 4s² (20)
- 3d¹⁰ (30)
- 4p⁶ (36)
- 5s² (38)
- 4d¹⁰ (48)
- 5p⁶ (54)
- 6s² (56)

At this point, we have filled 56 electrons.

### Step 4: Fill the 4f and 5d Orbitals
Next, we start filling the 4f and 5d orbitals. The 4f orbitals start filling after the 6s orbital:
- 4f can hold a maximum of 14 electrons, but we will fill it according to the periodic table:
- 4f¹ (57)
- 4f² (58)
- 4f³ (59)
- 4f⁴ (60)
- 4f⁵ (61)
- 4f⁶ (62)
- 4f⁷ (63)
- 5d¹ (64)

### Step 5: Write the Final Electronic Configuration
After filling the orbitals, we find that gadolinium has the following electronic configuration:
- 4f⁷ 5d¹ 6s²

### Conclusion
Thus, the electronic configuration of gadolinium (atomic number 64) is:
**4f⁷ 5d¹ 6s²**

---