Question

The wave functions of $1s$ orbitals of two hydrogen atoms are $\Psi_A$ and $\Psi_B$. $\Psi_A$ and $\Psi_B$ are linearly combined to form two molecular orbitals ($\sigma$ and $\sigma^{\ast}$). Which of the following statements are collect?
I. $\sigma^{*}$ is equal to $(\Psi_{A}-\Psi_{B})$.
II. In $\sigma$ - orbital, one nodal plane is present in between two nuclei.
III. The energy of $\sigma$ - orbital is lower than the energy of $\sigma^{*}$ -orbital.

• A. I ,II ,III
• B. I, II only
• C. II, III only
• D. I, III only

Answer 1

Answer: (D)

According to molecular orbital theory:

I. $\sigma^{*}$ -orbital are formed by the substraction of two wave functions say $\psi_{A}$ and $\psi_{B}$ and therefore $\sigma^{*}=\psi_{A}-\psi_{B}$

II. $\sigma$-orbital are formed when two orbitals are in same phase and thus, do not have nodal plane in between two nuclei.

III. Combination of two sigma $(\sigma)$ atomic orbitals given two molecular orbitals, out of which one is of lower energy called $\sigma$ bonding orbital and other is of higher energy called $\sigma^{*}$ anti-bonding orbital.

Hence, (i) and (iii) are the correct statements