To determine the correct electron configuration for an element with 5 electrons in the [tex]\( 3d \)[/tex] energy sublevel, we must follow the rules of electron configuration, specifically the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
### Step-by-Step Solution
1. Aufbau Principle: Electrons occupy the lowest energy orbital available first. The order in which energy levels are filled is known:
- [tex]\( 1s \)[/tex]
- [tex]\( 2s \)[/tex]
- [tex]\( 2p \)[/tex]
- [tex]\( 3s \)[/tex]
- [tex]\( 3p \)[/tex]
- [tex]\( 4s \)[/tex]
- [tex]\( 3d \)[/tex]
- [tex]\( 4p \)[/tex]
2. Electron Configuration Steps:
- Step 1: Fill the [tex]\( 1s \)[/tex] orbital: [tex]\( 1s^2 \)[/tex] (2 electrons)
- Step 2: Fill the [tex]\( 2s \)[/tex] orbital: [tex]\( 2s^2 \)[/tex] (2 electrons)
- Step 3: Fill the [tex]\( 2p \)[/tex] orbital: [tex]\( 2p^6 \)[/tex] (6 electrons)
- Step 4: Fill the [tex]\( 3s \)[/tex] orbital: [tex]\( 3s^2 \)[/tex] (2 electrons)
- Step 5: Fill the [tex]\( 3p \)[/tex] orbital: [tex]\( 3p^6 \)[/tex] (6 electrons)
- Step 6: Fill the [tex]\( 4s \)[/tex] orbital: [tex]\( 4s^2 \)[/tex] (2 electrons)
- Step 7: Begin filling the [tex]\( 3d \)[/tex] sublevel. We need 5 electrons in [tex]\( 3d \)[/tex]: [tex]\( 3d^5 \)[/tex]
### Total Electron Count and Configuration
We should now list the configuration up to the [tex]\( 3d \)[/tex] sublevel and ensure all prior sublevels are fully filled:
- [tex]\( 1s^2 \)[/tex]: 2 electrons
- [tex]\( 2s^2 \)[/tex]: 2 electrons
- [tex]\( 2p^6 \)[/tex]: 6 electrons
- [tex]\( 3s^2 \)[/tex]: 2 electrons
- [tex]\( 3p^6 \)[/tex]: 6 electrons
- [tex]\( 4s^2 \)[/tex]: 2 electrons
- [tex]\( 3d^5 \)[/tex]: 5 electrons
Adding these, the total number of electrons is [tex]\(2 + 2 + 6 + 2 + 6 + 2 + 5 = 25\)[/tex].
### Verification
The element with 5 electrons in the [tex]\( 3d \)[/tex] sublevel must have all the previous energy levels filled up to [tex]\( 3d \)[/tex]. Therefore, this matches with option C:
- [tex]\( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 \)[/tex]
Hence, the correct electron configuration is:
C. [tex]\( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 \)[/tex]
