To determine which of the given atoms have the same electron configuration, let's analyze each ion by converting it into its corresponding electron count based on the gain or loss of electrons:
1. [tex]$N ^{-3}$[/tex] (Nitrogen with a 3- charge):
- Neutral nitrogen atom (N) has 7 electrons.
- A 3- charge implies that it has gained 3 electrons.
- Therefore, the electron count is: [tex]\(7 + 3 = 10 \)[/tex] electrons.
2. [tex]$O ^{+2}$[/tex] (Oxygen with a 2+ charge):
- Neutral oxygen atom (O) has 8 electrons.
- A 2+ charge implies that it has lost 2 electrons.
- Therefore, the electron count is: [tex]\(8 - 2 = 6 \)[/tex] electrons.
3. [tex]$F ^{-1}$[/tex] (Fluorine with a 1- charge):
- Neutral fluorine atom (F) has 9 electrons.
- A 1- charge implies that it has gained 1 electron.
- Therefore, the electron count is: [tex]\(9 + 1 = 10 \)[/tex] electrons.
4. [tex]$Li ^{-1}$[/tex] (Lithium with a 1- charge):
- Neutral lithium atom (Li) has 3 electrons.
- A 1- charge implies that it has gained 1 electron.
- Therefore, the electron count is: [tex]\(3 + 1 = 4 \)[/tex] electrons.
5. [tex]$Be ^{+2}$[/tex] (Beryllium with a 2+ charge):
- Neutral beryllium atom (Be) has 4 electrons.
- A 2+ charge implies that it has lost 2 electrons.
- Therefore, the electron count is: [tex]\(4 - 2 = 2 \)[/tex] electrons.
Now let’s compare the electron counts to determine which ions have the same electron configuration:
- [tex]$N^{-3}$[/tex] has 10 electrons.
- [tex]$O^{+2}$[/tex] has 6 electrons.
- [tex]$F^{-1}$[/tex] has 10 electrons.
- [tex]$Li^{-1}$[/tex] has 4 electrons.
- [tex]$Be^{+2}$[/tex] has 2 electrons.
From the above, we can see:
- [tex]$N^{-3}$[/tex] and [tex]$F^{-1}$[/tex] both have 10 electrons.
Therefore, the ions that have the same electron configuration are:
- [tex]$N^{-3}$[/tex] and [tex]$F^{-1}$[/tex].
