To determine which of the given electron configurations is reasonable, let's break down the steps to ensure it adheres to the principles of electron configuration in atomic structure.
### Key Principles of Electron Configuration:
1. Principle Quantum Levels (n): Electrons fill atomic orbitals starting from the lowest energy level to the highest.
2. Sublevels and Orbitals:
- The sublevels are s, p, d, and f.
- The number of orbitals and maximum capacity of electrons in sublevels:
- S sublevel: 1 orbital, maximum 2 electrons.
- P sublevel: 3 orbitals, maximum 6 electrons.
- D sublevel: 5 orbitals, maximum 10 electrons.
- F sublevel: 7 orbitals, maximum 14 electrons.
### Given Options:
1. [tex]$1s^2 1p^6 2d^2$[/tex]
2. [tex]$1s^2 2s^4 2p^6$[/tex]
3. [tex]$1s^2 2s^2 2p^5$[/tex]
4. [tex]$1s^2 2s^2 2d^6$[/tex]
### Analysis of Each Option:
1. [tex]$1s^2 1p^6 2d^2$[/tex]:
- There is no 'p' sublevel for the principal quantum number 1 (n=1).
- The correct sequence does not have "1p".
2. [tex]$1s^2 2s^4 2p^6$[/tex]:
- The 's' sublevel can only hold a maximum of 2 electrons.
- "2s^4" violates this rule because s can only hold up to 2 electrons.
3. [tex]$1s^2 2s^2 2p^5$[/tex]:
- 1s sublevel holds 2 electrons (correct).
- 2s sublevel holds 2 electrons (correct).
- The 2p sublevel can hold up to 6 electrons, and having 5 electrons (2p^5) is within this limit.
- This sequence follows the proper rules for electron configurations, making it reasonable.
4. [tex]$1s^2 2s^2 2d^6$[/tex]:
- There is no 'd' sublevel for the principal quantum number 2 (n=2).
- The 'd' sublevels start from n=3 (3d). The existence of "2d" is invalid.
### Conclusion:
Among the given options, the only electron configuration that follows the correct principles of atomic structure and electron configuration is:
[tex]$1s^2 2s^2 2p^5$[/tex]
