Question

The bond energy order of $H{{e}^{+2}}$and $He{{H}^{+}}$ is:
(A) $H{{e}^{+2}}>He{{H}^{+}}$
(B) $He{{H}^{+}}=H{{e}^{+2}}$
(C) $He{{H}^{+}}>H{{e}^{2+}}$
(D)None of the above

Answer 1

Hint: Bond order is one half of the difference between the number of electrons in bonding and antibonding orbitals. Helium atom contains two electrons. A positive bond order means stable molecule and negative or zero bond order means an unstable molecule. In helium hydride ions, a helium atom is bonded to hydrogen and one electron is removed.

Complete step by step solution:
The molecular orbital theory has salient features:
-electrons in a molecule are present in various molecular orbitals as electrons of atoms are present in the various atomic orbitals.
-the atomic orbitals having comparable energies and proper symmetry combine to form molecular orbitals.
-While an electron in an atomic orbital is attracted by one nucleus, in molecular orbital electrons are attracted by two or more nuclei.
-number of molecular orbitals formed is equal to the number of combining atomic orbitals. When two atomic orbitals combine, two molecular orbitals are formed known as bonding molecular orbital and antibonding molecular orbital.
-bonding molecular orbital has lower energy and greater stability than antibonding molecular orbital.
-molecular orbitals are filled in accordance with Aufbau principle obeying Pauli’s exclusion and Hund’s rule.
- Bond order is one half of the difference between the number of electrons in bonding and antibonding orbitals.
-in $H{{e}^{+2}}$, number of electrons in bonding and antibonding orbitals are 2 so bond order is $\frac{1}{2}\left( {{N}_{b}}-{{N}_{a}} \right)$
-In $He{{H}^{+}}$,number of electrons in bonding orbital are 3 and number of electrons in antibonding orbitals are 1 so bond order is $=\frac{1}{2}\left( 3-1 \right)=1$.

So The bond energy order of $H{{e}^{+2}}$and $He{{H}^{+}}\]is (C) \[He{{H}^{+}}>H{{e}^{+2}}$.

Note: Helium atom contains two electrons. A positive bond order means stable molecule and negative or zero bond order means an unstable molecule. In helium hydride ions, helium atoms are bonded to hydrogen and one electron is removed. The number of electrons. bond order can be calculated using formula =$\frac{1}{2}\left( {{N}_{b}}-{{N}_{a}} \right)$. -bonding molecular orbital has lower energy and greater stability than antibonding molecular orbital. molecular orbitals are filled in accordance with Aufbau principle obeying Pauli’s exclusion and Hund’s rule. Bond order is one half of the difference between the number of electrons in bonding and antibonding orbitals.