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The correct statement with regard to $ H_{2}^{+} $ and $ H_{2}^{-} $
(A) Both $ H_{2}^{+} $ and $ H_{2}^{-} $ are equally stable
(B) Both $ H_{2}^{+} $ and $ H_{2}^{-} $ do not exist
(C) $ H_{2}^{-} $ is more stable than $ H_{2}^{+} $
(D) $ H_{2}^{+} $ is more stable than $ H_{2}^{-} $

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Last updated date: 20th Jul 2024
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Answer
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Hint :The composition of $ H_{2}^{+} $ and $ H_{2}^{-} $ defines the stability order. $ H_{2}^{+} $ does not include any electron in the antibonding molecular orbital. $ H_{2}^{-} $ includes electrons in antibonding molecular orbital.The stability can be easily identified from the electron presence in bonding and antibonding molecular orbital.

Complete Step By Step Answer:
The electron presence in anti-bonding orbital result in repulsion and decrease of stability
The stability order follows the molecular orbital theory
The formula for bonding order can be regarded as follows
Bonding order $ =\dfrac{1}{2} $ (Number of bonding electrons -Number of antibonding electrons)
The number of antibonding electrons in $ H_{2}^{+} $ is 0
The number of antibonding electrons in $ H_{2}^{-} $ is 1
The bonding order of $ H_{2}^{+} $ is $ ~ $ $ =\dfrac{1}{2}(1-0)=0.5 $
The bonding order of $ H_{2}^{-} $ is $ =\dfrac{1}{2}(2-1)=0.5 $
 $ H_{2}^{+} $ and $ H_{2}^{-} $ molecule have the same bond order
Presence of anti-bonding electron decreases the stability of the molecule
Therefore, $ H_{2}^{+} $ is more stable than $ H_{2}^{-} $
Both $ H_{2}^{+} $ and $ H_{2}^{-} $ are equally stable is incorrect statement
Both $ H_{2}^{+} $ and $ H_{2}^{-} $ do not exist is incorrect statement
 $ H_{2}^{-} $ is more stable than $ H_{2}^{+} $ is incorrect statement
The correct statement is $ H_{2}^{+} $ is more stable than $ H_{2}^{-} $
Due to the electron-electron repulsion in $ H_{2}^{-} $ , the stability of $ H_{2}^{-} $ is low
The configuration of $ H_{2}^{+} $ is $ 1 $ electron in $ 1 $ s bonding orbital
The configuration of $ H_{2}^{-} $ is $ 1 $ electron in $ 1 $ s bonding orbital and $ 1 $ electron in $ 1 $ s antibonding orbital
Even though the bond order of both $ H_{2}^{+} $ and $ H_{2}^{-} $ are same, the stability is different
Therefore, $ H_{2}^{+}>H_{2}^{-} $ .

Note :
The stability order follows the molecular orbital theory. The electron presence in anti-bonding orbital results in repulsion and decrease of stability. Electron-electron repulsion in $ H_{2}^{-} $ , the stability of $ H_{2}^{-} $ is low.