Chapter 29, Problem 4Q

To determine

The reason why the molecule $H_3$ is not stable, but the ion $H_3{}^{+}$ is

Answer to Problem 4Q

Solution:

The correct answer is ‘to obey Pauli Exclusion Principle’.

Explanation of Solution

Given:

The $H_3$ molecule is not stable but the ion $H_3{}^{+}$ is.

Formula used:

• $\underset{\_}{PauliExclusionprinciple}:-$ No two electrons (or any other fermions)of an atom or molecule, can have all the same electronic quantum numbers $\left(n,l,m_l,m_s\right)$.

Calculation:

As we know that hydrogen atom has only one S-orbital and in each S-orbital a maximum of 2 electrons can be accommodated.

Now, the atomic number of hydrogen atom can share its electron with other hydrogen atom to form a covalent bond.

In this way the electronic quantum numbers of such two atoms will have the same value for n, l, and $m_l$, while $m_s$ will be $+\frac{1}{2}$ for one atom and $-\frac{1}{2}$ for other atom.

Now, if we consider a third hydrogen atom that will have all n, l,$m_l$ and $m_s$ to be the same as that of any of previous two atoms; it is not possible according to the Pauli Exclusion Principle.

When we consider $H_3{}^{+}$ ion, the electron of one atom is removed. So, now it does not over-rule the Pauli Exclusion Principle. Thus it is found to be stable.