To determine the correct formula for a chromate ion that consists of four oxygen atoms bonded to a chromium atom and has two extra electrons, we will analyze each given option.
### Analysis of Options
1. Option 1: [tex]$Cr _4 O ^{2-}$[/tex]
This formula suggests that there are four chromium atoms and one oxygen atom with an overall 2- charge. However, a chromate ion typically consists of one chromium atom and four oxygen atoms. Therefore, this option is not correct.
2. Option 2: [tex]$CrO_4^{2+}$[/tex]
This formula indicates that there is one chromium atom and four oxygen atoms, but with a 2+ charge. However, a chromate ion has two extra electrons, resulting in a 2- charge instead of a 2+ charge. Thus, this option is incorrect.
3. Option 3: [tex]$CrO_4^{2-}$[/tex]
This formula shows one chromium atom bonded to four oxygen atoms, with an overall 2- charge. This fits the description perfectly since the chromate ion has four oxygen atoms and two extra electrons, resulting in the 2- charge.
### Conclusion
The correct formula for a chromate ion, consisting of four oxygen atoms bonded to a chromium atom and two extra electrons, is:
[tex]$
CrO_4^{2-}
$[/tex]
Thus, the correct option is:
[tex]$
\boxed{CrO_4^{2-}}
$[/tex]
