JEE Advance - Chemistry (2017 - Paper 1 Offline - No. 9)
Among $${H_2},H{e_2}^ + ,L{i_2},$$ $$B{e_2},{B_2},{C_2},{N_2},O_2^ - $$ and $${F_2},$$ the number of diamagnetic species is
(Atomic numbers : $$H = 1,He = 2,$$ $$Li = 3,Be = 4,$$ $$B = 5,C = 6,$$ $$N = 7,$$ $$O = 8,F = 9$$)
(Atomic numbers : $$H = 1,He = 2,$$ $$Li = 3,Be = 4,$$ $$B = 5,C = 6,$$ $$N = 7,$$ $$O = 8,F = 9$$)
Answer
6
Explanation
(1) Electronic configuration of diatomic $\mathrm{H}_2$ on the the basis of molecular orbital theory:
$\left(\sigma_{1 \mathrm{~s}}\right)^2\left(\sigma_{1 s}^*\right)^0$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(2) Electronic configuration of diatomic $\mathrm{He}^{2+}$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^1$
There is one unpaired electron in the sigma bonding molecular orbital; hence, it's a paramagnetic molecule.
(3) Electronic configuration of diatomic $\mathrm{Li}_2$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(4) Electronic configuration of diatomic $\mathrm{Be}_2$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{1 s}^*\right)^2$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(5) Electronic configuration of diatomic $B_2$ on the basis of molecular orbitals theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) $$
There are two unpaired electrons in pi bonding molecular orbital; hence, it's a paramagnetic molecule.
(6) Electronic configuration of diatomic $\mathrm{C}_2$ on the basis of molecular orbital theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^2 \equiv \pi_{2 p y}^2\right) $$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(7) Electronic configuration of diatomic $\mathrm{N}_2$ on the basis of molecular orbital theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) \sigma_{2 p z}^2 $$
There are no unpaired electron in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(8) Electronic configuration of diatomic $\mathrm{O}_2$ on the basis of molecular orbital theory:
$$ \begin{aligned} & \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\sigma_{p 3}^2\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) \\\\ & \left(\pi_{2 p x}^* \equiv \pi\right) \end{aligned} $$
There is one unpaired electron in the $\mathrm{pi}^*$ anti-bonding molecular orbital; hence, it's a paramagnetic molecule.
(9) Electronic configuration of diatomic $\mathrm{F}_2$ on the basis of molecular orbital theory:
$$ \begin{aligned} & \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\sigma_{2 p z}\right)^2\left(\pi_{2 p x}^2 \equiv \pi_{2 p y}^2\right) \\\\ & \left(\pi_{2 p x}^{2^*} \equiv \pi_{2 p y}^{2^*}\right) \end{aligned} $$
All the electrons are paired in the bonding and anti-bonding molecular orbitals; hence, $\mathrm{F}_2$ is a diamagnetic molecule
Answer. The are 6 diamagnetic species among the given diatomic molecules.
$\left(\sigma_{1 \mathrm{~s}}\right)^2\left(\sigma_{1 s}^*\right)^0$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(2) Electronic configuration of diatomic $\mathrm{He}^{2+}$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^1$
There is one unpaired electron in the sigma bonding molecular orbital; hence, it's a paramagnetic molecule.
(3) Electronic configuration of diatomic $\mathrm{Li}_2$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(4) Electronic configuration of diatomic $\mathrm{Be}_2$ on the basis of molecular orbital theory:
$\left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{1 s}^*\right)^2$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(5) Electronic configuration of diatomic $B_2$ on the basis of molecular orbitals theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) $$
There are two unpaired electrons in pi bonding molecular orbital; hence, it's a paramagnetic molecule.
(6) Electronic configuration of diatomic $\mathrm{C}_2$ on the basis of molecular orbital theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^2 \equiv \pi_{2 p y}^2\right) $$
There are no unpaired electrons in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(7) Electronic configuration of diatomic $\mathrm{N}_2$ on the basis of molecular orbital theory:
$$ \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) \sigma_{2 p z}^2 $$
There are no unpaired electron in the bonding and anti-bonding molecular orbitals; hence, it's a diamagnetic molecule.
(8) Electronic configuration of diatomic $\mathrm{O}_2$ on the basis of molecular orbital theory:
$$ \begin{aligned} & \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\sigma_{p 3}^2\right)^2\left(\pi_{2 p x}^1 \equiv \pi_{2 p y}^1\right) \\\\ & \left(\pi_{2 p x}^* \equiv \pi\right) \end{aligned} $$
There is one unpaired electron in the $\mathrm{pi}^*$ anti-bonding molecular orbital; hence, it's a paramagnetic molecule.
(9) Electronic configuration of diatomic $\mathrm{F}_2$ on the basis of molecular orbital theory:
$$ \begin{aligned} & \left(\sigma_{1 s}\right)^2\left(\sigma_{1 s}^*\right)^2\left(\sigma_{2 s}\right)^2\left(\sigma_{2 s}^*\right)^2\left(\sigma_{2 p z}\right)^2\left(\pi_{2 p x}^2 \equiv \pi_{2 p y}^2\right) \\\\ & \left(\pi_{2 p x}^{2^*} \equiv \pi_{2 p y}^{2^*}\right) \end{aligned} $$
All the electrons are paired in the bonding and anti-bonding molecular orbitals; hence, $\mathrm{F}_2$ is a diamagnetic molecule
Answer. The are 6 diamagnetic species among the given diatomic molecules.
Comments (0)
