Which of the following decomposition reactions is NOT a redox reaction?

The correct option is Decomposition of calcium carbonate.

To determine which decomposition reaction is not a redox reaction, we examine the changes in oxidation states of the elements involved in each reaction. A redox reaction is characterized by a transfer of electrons, which leads to a change in the oxidation states of atoms. If there is no change in oxidation states, the reaction is not a redox reaction.

Let's analyze the decomposition of calcium carbonate (${\mathrm{CaCO}}_3$):

The chemical equation for this thermal decomposition is:
${\mathrm{CaCO}}_3\to \mathrm{CaO}+{\mathrm{CO}}_2$

Let's determine the oxidation states of each element before and after the reaction:
- Calcium (Ca): In the reactant ${\mathrm{CaCO}}_3$, the oxidation state of Ca is +2. In the product $\mathrm{CaO}$, it remains +2. (No change)
- Carbon (C): In the reactant ${\mathrm{CaCO}}_3$, the oxidation state of C is +4. In the product ${\mathrm{CO}}_2$, it remains +4. (No change)
- Oxygen (O): In the reactant ${\mathrm{CaCO}}_3$, the oxidation state of O is -2. In both products $\mathrm{CaO}$ and ${\mathrm{CO}}_2$, it remains -2. (No change)

Since the oxidation states of all the atoms remain constant throughout the reaction, this is a non-redox decomposition reaction.

For comparison, let's examine the other options:

- Decomposition of sodium hydride:
$2\mathrm{NaH}\to 2\mathrm{Na}+H_2$
In this reaction, the oxidation state of Na changes from +1 to 0 (reduction), and H changes from -1 to 0 (oxidation). Thus, it is a redox reaction.

- Decomposition of potassium chlorate:
$2{\mathrm{KClO}}_3\to 2\mathrm{KCl}+3O_2$
In this reaction, the oxidation state of Cl changes from +5 to -1 (reduction), and O changes from -2 to 0 (oxidation). Thus, it is a redox reaction.

- Decomposition of dihydrogen monoxide (water):
$2H_{2}O\to 2H_2+O_2$
In this reaction, the oxidation state of H changes from +1 to 0 (reduction), and O changes from -2 to 0 (oxidation). Thus, it is a redox reaction.