To determine which of the given outer electron configurations could belong to a noble gas, we need to understand the electron configuration of noble gases. Noble gases are elements in Group 18 of the periodic table, and they have completely filled electron shells, which make them very stable. The general outer electron configurations of noble gases are:
- For helium (He): [tex]\(1s^2\)[/tex]
- For neon (Ne) and the following noble gases: [tex]\(ns^2 np^6\)[/tex], where [tex]\(n\)[/tex] represents the principal quantum number of the outermost shell.
Now, let's evaluate each given configuration:
1. [tex]\(n s^2\)[/tex] - This configuration indicates there are 2 electrons in the [tex]\( s \)[/tex]-orbital of the outermost shell. However, it does not include the p-orbital, which means it is not fully filled as required for a noble gas configuration (except for helium). Therefore, this configuration cannot belong to a noble gas beyond helium.
2. [tex]\(n s^2 n p^5\)[/tex] - This configuration suggests there are 2 electrons in the [tex]\( s \)[/tex]-orbital and 5 electrons in the [tex]\( p \)[/tex]-orbital of the outermost shell, totaling 7 outer electrons. Noble gases beyond helium have a completely filled [tex]\(p\)[/tex]-orbital with 6 electrons, so this configuration cannot belong to a noble gas.
3. [tex]\(n s^2 n p^6\)[/tex] - This configuration indicates 2 electrons are in the [tex]\( s \)[/tex]-orbital and 6 electrons in the [tex]\( p \)[/tex]-orbital, yielding a total of 8 outer electrons. This matches the electron configuration of a noble gas beyond helium, which has fully filled [tex]\( s \)[/tex]- and [tex]\( p \)[/tex]-orbitals in the outer shell. Therefore, this configuration can belong to a noble gas.
4. [tex]\(n s^2 n p^2\)[/tex] - This configuration indicates there are 2 electrons in the [tex]\( s \)[/tex]-orbital and 2 electrons in the [tex]\( p \)[/tex]-orbital of the outermost shell. This is not a fully filled outer shell, as noble gases require 6 electrons in the [tex]\( p \)[/tex]-orbital. Therefore, this configuration cannot belong to a noble gas.
Thus, the outer electron configuration that could belong to a noble gas is:
[tex]\[ n s^2 n p^6 \][/tex]
Hence, the configuration that corresponds to a noble gas is option 3: [tex]\(n s^2 n p^6\)[/tex].
