To solve the question of what [tex]\( X \)[/tex] represents in the given electron configuration for an atom with 14 electrons, let's follow a step-by-step process:
1. Identify Total Electrons Represented:
- The atom in question has a total of 14 electrons.
2. Analyze the Provided Configuration:
- The given partial electron configuration is [tex]\( 1s^2 2s^2 2p^6 3s^2 \)[/tex].
- We need to determine how many electrons are accounted for in this partial configuration.
3. Count the Electrons in Each Sublevel:
- [tex]\( 1s^2 \)[/tex]: This means there are 2 electrons in the 1s orbital.
- [tex]\( 2s^2 \)[/tex]: This means there are 2 electrons in the 2s orbital.
- [tex]\( 2p^6 \)[/tex]: This means there are 6 electrons in the 2p orbitals.
- [tex]\( 3s^2 \)[/tex]: This means there are 2 electrons in the 3s orbital.
4. Sum the Electrons:
- Total electrons in the provided configuration: [tex]\( 2 (1s^2) + 2 (2s^2) + 6 (2p^6) + 2 (3s^2) = 12 \)[/tex] electrons.
5. Determine Remaining Electrons:
- The atom has a total of 14 electrons, and the partial configuration accounts for 12 of them.
- Therefore, there are [tex]\( 14 - 12 = 2 \)[/tex] electrons yet to be placed in an appropriate orbital.
6. Identify Next Available Energy Level:
- The next available orbitals after [tex]\( 3s \)[/tex] are the [tex]\( 3p \)[/tex] orbitals because the [tex]\( p \)[/tex] orbitals in any given principal energy level come after the [tex]\( s \)[/tex] orbital.
7. Place the Remaining Electrons:
- The 2 remaining electrons will occupy the [tex]\( 3p \)[/tex] orbital.
8. Determine [tex]\( X \)[/tex] in the Configuration:
- Therefore, [tex]\( X = 3p^2 \)[/tex].
9. Match [tex]\( X \)[/tex] with the Given Options:
- Among the provided options:
- [tex]\( 2d^2 \)[/tex] is not possible because [tex]\( d \)[/tex] orbitals start from the 3rd principal energy level.
- [tex]\( 3s^2 \)[/tex] is already occupied in the given configuration.
- [tex]\( 3p^2 \)[/tex] matches our requirement perfectly.
- [tex]\( 4s^2 \)[/tex] would be the next level after [tex]\( 3p \)[/tex] and not appropriate here.
Therefore, [tex]\( X \)[/tex] represents [tex]\( 3p^2 \)[/tex], corresponding to the third multiple-choice option:
[tex]\[
\boxed{3p^2}
\][/tex]
Thus, the correct multiple-choice option is:
[tex]\[
\boxed{3}
\][/tex]
