Number of Unpaired Electrons in Gd(64)

Gadolinium (Gd) is a transition metal with the atomic number 64. To determine the number of unpaired electrons in Gd(64), we need to understand the electron configuration of gadolinium.

1. Electron Configuration of Gadolinium:
The electron configuration of an atom describes the arrangement of electrons in its energy levels or shells. The electron configuration of gadolinium can be determined by using the Aufbau principle, which states that electrons fill the lowest energy levels first.

The electron configuration of gadolinium is [Xe] 4f^7 5d^1 6s^2, where [Xe] represents the electron configuration of the noble gas xenon.

2. Filling of Electrons in Orbital Diagram:
To determine the number of unpaired electrons, we need to fill the electrons in the orbital diagram.

- In the f sublevel, there are 7 electrons (4f^7).
- In the d sublevel, there is 1 electron (5d^1).
- In the s sublevel, there are 2 electrons (6s^2).

3. Hund's Rule:
According to Hund's rule, electrons occupy orbitals of the same energy singly, with parallel spins, before pairing up. This maximizes the total spin, resulting in greater stability.

- In the f sublevel, there are 7 electrons. Since there are only 7 orbitals available, all of them will be singly occupied with parallel spins, resulting in 7 unpaired electrons.
- In the d sublevel, there is 1 electron. This electron will be singly occupied with a parallel spin, resulting in 1 unpaired electron.
- In the s sublevel, there are 2 electrons. These electrons will be paired up, resulting in 0 unpaired electrons.

4. Calculating the Total Number of Unpaired Electrons:
To calculate the total number of unpaired electrons, we sum up the number of unpaired electrons in each sublevel.

- Unpaired f electrons: 7
- Unpaired d electrons: 1
- Unpaired s electrons: 0

Therefore, the total number of unpaired electrons in Gd(64) is 7 + 1 + 0 = 8.

Conclusion:
The correct answer is 8. Gadolinium (Gd) with the atomic number 64 has a total of 8 unpaired electrons.