To determine the electron configuration for Calcium ([tex]\(Ca\)[/tex]) and Promethium ([tex]\(Pm\)[/tex]) in noble-gas notation, let’s follow these steps:
### Electron Configuration for Calcium (Ca)
1. Identify the Position of Calcium in the Periodic Table:
- Calcium is in Group 2 and Period 4 of the periodic table.
2. Determine the Nearest Noble Gas Preceding Calcium:
- The noble gas preceding Calcium is Argon ([tex]\(Ar\)[/tex]).
3. Write the Noble-Gas Configuration:
- Argon has the electron configuration [tex]\( [Ne] 3s^2 3p^6 \)[/tex], but we use [tex]\( [Ar] \)[/tex] to represent this configuration.
4. Add the Remaining Electrons:
- Calcium has 20 electrons in total.
- After Argon ([tex]\(18\)[/tex] electrons), the next [tex]\(2\)[/tex] electrons go into the [tex]\(4s\)[/tex] orbital.
[tex]\[
Ca: [Ar] 4s^2
\][/tex]
Therefore, the correct noble-gas notation for Calcium:
[tex]\[
Ca: [Ar] 4s^2
\][/tex]
### Electron Configuration for Promethium (Pm)
1. Identify the Position of Promethium in the Periodic Table:
- Promethium is in the Lanthanides series.
2. Determine the Nearest Noble Gas Preceding Promethium:
- The noble gas preceding Promethium is Xenon ([tex]\(Xe\)[/tex]).
3. Write the Noble-Gas Configuration:
- Xenon has the electron configuration [tex]\( [Kr] 4d^{10} 5s^2 5p^6 \)[/tex], but we use [tex]\( [Xe] \)[/tex] to represent this configuration.
4. Add the Remaining Electrons:
- Promethium ([tex]\(Pm\)[/tex]) has [tex]\(61\)[/tex] electrons in total.
- After Xenon ([tex]\(54\)[/tex] electrons), the next electrons are distributed in the [tex]\(4f\)[/tex] and [tex]\(6s\)[/tex] orbitals.
- Promethium's configuration is [tex]\( 4f^5 6s^2 \)[/tex].
[tex]\[
Pm: [Xe] 4f^5 6s^2
\][/tex]
Therefore, the correct noble-gas notation for Promethium:
[tex]\[
Pm: [Xe] 4f^5 6s^2
\][/tex]
### Conclusion
For the given options:
- For Calcium ([tex]\(Ca\)[/tex]):
- [tex]\([Ar] 4s^2\)[/tex] is the correct noble-gas notation.
- For Promethium ([tex]\(Pm\)[/tex]), although options are not explicitly given, the correct noble-gas notation is:
- [tex]\([Xe] 4f^5 6s^2\)[/tex].
In summary, the noble-gas notation for the elements are:
- [tex]\(Ca\)[/tex]: [tex]\([Ar] 4s^2\)[/tex]
- [tex]\(Pm\)[/tex]: [tex]\([Xe] 4f^5 6s^2\)[/tex]
The correct answer for Calcium is: [tex]\([Ar] 4s^2\)[/tex].
