To determine the electron configurations for the potassium ion (K[tex]\(^+\)[/tex]) and the bromine ion (Br[tex]\(^{-}\)[/tex]), follow these steps:
### Step-by-Step Solution for Potassium Ion (K[tex]\(^+\)[/tex]):
1. Find the atomic number of Potassium (K):
- Potassium has an atomic number of 19, meaning it has 19 electrons in its neutral state.
2. Write the electron configuration for neutral Potassium (K):
- The electron configuration for potassium can be written as:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 4s^1
\][/tex]
3. Determine the electron configuration for Potassium ion (K[tex]\(^+\)[/tex]):
- A potassium ion (K[tex]\(^+\)[/tex]) has lost one electron. This means it has 18 electrons instead of 19.
- The electron is lost from the outermost shell, which in this case is the 4s orbital.
- The electron configuration now becomes:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6
\][/tex]
### Step-by-Step Solution for Bromine Ion (Br[tex]\(^{-}\)[/tex]):
1. Find the atomic number of Bromine (Br):
- Bromine has an atomic number of 35, meaning it has 35 electrons in its neutral state.
2. Write the electron configuration for neutral Bromine (Br):
- The electron configuration for bromine can be written as:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 3d^{10} \; 4s^2 \; 4p^5
\][/tex]
3. Determine the electron configuration for Bromine ion (Br[tex]\(^{-}\)[/tex]):
- A bromine ion (Br[tex]\(^{-}\)[/tex]) has gained one electron. This means it has 36 electrons instead of 35.
- The additional electron is added to the outermost shell, which in this case is the 4p orbital.
- The electron configuration now becomes:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 3d^{10} \; 4s^2 \; 4p^6
\][/tex]
### Conclusion:
- The electron configuration of a potassium ion (K[tex]\(^+\)[/tex]) is:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6
\][/tex]
- The electron configuration of a bromine ion (Br[tex]\(^{-}\)[/tex]) is:
[tex]\[
1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^6 \; 3d^{10} \; 4s^2 \; 4p^6
\][/tex]
These configurations reflect that the potassium ion achieves the electron configuration of argon (Ar) and the bromine ion achieves the electron configuration of krypton (Kr), making both ions more stable.
