Question

The bond order of \[H_2^ - \] ions is \[\dfrac{1}{2}\]. If it has two bonding electrons, calculate the number of antibonding electrons.
A.\[4\]
B.\[3\]
C.\[2\]
D.\[1\]

Answer 1

Hint: We have to know that the bond order will appear the total number of chemical bonds which is present between a pair of atoms. And the bond order can be calculated by taking half of the difference between the number of bonding electrons and number of antibonding electrons present in bonding orbitals and antibonding orbital respectively. And this term is defined by the scientist Linus Pauling.

Complete answer:
The number of anti-bonding present in the hydrogen ion is not equal to four. Hence, option (A) is incorrect.
The formula of bond order is used to calculate the number of antibonding electrons present in hydrogen ions and it will not be equal to three. Hence, the option (B) is incorrect.
The antibonding electron present in hydrogen ions with bond order \[\dfrac{1}{2}\], is not equal to two Hence, option (C) is incorrect.
According to the question, the bond order of hydrogen is equal to \[\dfrac{1}{2}\]. And the number of bonding electrons present in hydrogen ions is equal to two.
Therefore, the number of anti- bonding electrons present in the hydrogen ion can be found out by using the formula of bond order. The bond order is equal to half of the difference between the bonding electron and anti- bonding electron. And the equation can be written as,
\[Bond\,order = \dfrac{1}{2}\left( {{N_b} - {N_a}} \right)\]
Where, \[{N_b}\]is the number of bonding electrons.
\[{N_a}\]is the number of antibonding electron
Substitute the given values in the above equation,
\[\dfrac{1}{2} = \dfrac{1}{2}\left( {2 - {N_a}} \right)\]
By rearranging the equation, will get the value of \[{N_a}\]
\[{N_a} = 2 - 1 = 1\]
Therefore, the number of antibonding electrons present in \[H_2^ - \] is equal to one.

Hence, the option (D) is correct.

Note:
We must have to know that the bond order is the difference between both bonding and anti- bonding electrons and it is always a stable electron that has the positive value of bond order. The bonding electrons which participate in the chemical bonding and it is present in the bonding molecular orbital. The antibonding electrons are occupied in the antibonding molecular orbitals.