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. ${\sigma }^{\ast }$ 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 ${\sigma }^{\ast }$ -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. ${\sigma }^{\ast }$ -orbital are formed by the substraction of two wave functions say ${\psi }_A$ and ${\psi }_B$ and therefore ${\sigma }^{\ast }={\psi }_A-{\psi }_B$

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 ${\sigma }^{\ast }$ anti-bonding orbital.

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