To determine the correct abbreviated form of the electron configuration for Cadmium (Cd), which has an atomic number of 48, we'll go through the process of electron configuration step by step.
1. Identify the base noble gas: We look for the noble gas preceding Cadmium in the periodic table. Cadmium (Cd) is in period 5. The preceding noble gas is Krypton (Kr), which is in period 4.
2. Start from the noble gas core: The electron configuration starting from Krypton ([Kr]) includes all the electrons up to Krypton. The electron configuration of Krypton is:
- [Kr] = [tex]$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6$[/tex].
3. Add remaining electrons to complete the configuration for Cadmium: After the configuration of Krypton, we need to add the electrons that go beyond Krypton to reach Cadmium (Cd). Cadmium needs a total of 48 electrons and Krypton already accounts for 36 of these.
According to the periodic table, the electrons are added in the following order:
- After the electrons accounted for by Krypton, the next electrons fill the 5s orbital.
- Next, the electrons fill the 4d orbital.
Putting this together,
- The 5s subshell can hold 2 electrons: [tex]$5s^2$[/tex].
- The 4d subshell can hold 10 electrons: [tex]$4d^{10}$[/tex].
Therefore, the electron configuration for Cadmium beyond Krypton is:
- [tex]$[Kr] 4d^{10} 5s^2$[/tex].
4. Match with the given options:
- (A) [tex]$[ Kr ] 5 s^2 5 d^{10}$[/tex]: This option is incorrectly placing the 5d orbital, which does not belong in this configuration.
- (B) [tex]$[ Xe ] 4 d^{10} 5 s^2$[/tex]: This option incorrectly uses Xenon (Xe) instead of Krypton (Kr).
- (C) [tex]$[ Kr ] 4 d^{10} 5 s^2$[/tex]: This matches our computed configuration.
- (D) [tex]$[ Xe ] 5 s^2 5 d^{10}$[/tex]: Similar to option B, this incorrectly uses Xenon and misplaces orbitals.
Based on these examinations, the correct abbreviated form of the electron configuration for Cadmium (Cd) is:
Option (C) [tex]$[ Kr ] 4 d^{10} 5 s^2$[/tex]
