The question asks us to identify which of the given methods cannot be used to obtain oxygen gas.

Understanding Different Methods for Oxygen Preparation

Let's analyze each option to determine if oxygen is produced.

Method 1: Heating Potassium Perchlorate ($ \text{KClO}_4 $)

Heating potassium perchlorate at high temperatures (around 650°C) causes it to decompose and release oxygen gas. The chemical reaction is:

\( 2\text{KClO}_4 (\text{s}) \xrightarrow{650^\circ\text{C}} 2\text{KCl}(\text{s}) + 4\text{O}_2 (\text{g}) \)

This reaction is a valid method to obtain oxygen.

Method 2: Strongly Heating Copper Hydroxide ($ \text{Cu(OH)}_2 $)

When copper(II) hydroxide is heated strongly, it undergoes thermal decomposition. The products formed are copper(II) oxide and water vapor. The reaction is:

\( \text{Cu(OH)}_2 (\text{s}) \xrightarrow{\Delta} \text{CuO}(\text{s}) + \text{H}_2\text{O}(\text{g}) \)

Based on this primary decomposition, oxygen gas is not directly produced.

Method 3: Action of Concentrated $ \text{H}_2\text{SO}_4 $ on $ \text{MnO}_2 $

The reaction between concentrated sulfuric acid and manganese dioxide ($ \text{MnO}_2 $) is not a standard method for the preparation of oxygen gas. While manganese dioxide can act as an oxidizing agent and hot concentrated sulfuric acid is also an oxidizing agent, their reaction typically leads to the formation of manganese sulfates or other products, depending on the conditions. Oxygen gas is not a significant or primary product of this reaction under typical conditions.

Method 4: Action of Water on Ozone ($ \text{O}_3 $)

Ozone ($ \text{O}_3 $) is an allotrope of oxygen that is relatively unstable and tends to decompose into oxygen ($ \text{O}_2 $). The presence of water can catalyze or facilitate the decomposition of ozone to form oxygen gas:

\( 2\text{O}_3 (\text{g}) \xrightarrow{\text{H}_2\text{O}} 3\text{O}_2 (\text{g}) \)

This method can be used to obtain oxygen.

Conclusion on Oxygen Production Methods

Reviewing the options, methods 1 and 4 are known ways to produce oxygen gas. Method 2, heating copper hydroxide, primarily produces copper oxide and water. Method 3, the action of concentrated sulfuric acid on manganese dioxide, does not typically result in the production of oxygen gas under standard conditions.

Therefore, oxygen cannot be obtained by the action of concentrated $ \text{H}_2\text{SO}_4 $ on $ \text{MnO}_2 $ as a primary method for its preparation.