Nitrogen cannot be obtained by heating
(a) \[Pb{{({{N}_{3}})}_{2}}(s)\]
(b) \[KN{{O}_{3}}\]
(c) \[{{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}(s)\]
(d) \[N{{H}_{4}}N{{O}_{2}}(s)\]

Hint: Nitrogen makes up the 78% of the air that breathes in. Nitrogen is also released during volcanic eruption. Nitrogen is produced commercially from air by the process of fractional distillation. If we pass ammonia gas over a hot metallic oxide then formation of nitrogen gas occurs.

Complete step by step solution:
When \[Pb{{({{N}_{3}})}_{2}}(s)\] is heated it gives nitrogen and lead. We can see this by the following equation
\[N{{H}_{4}}N{{O}_{2}}(s)\to {{N}_{2}}+2{{H}_{2}}O\] \[Pb{{({{N}_{3}})}_{2}}(s)\to Pb+3{{N}_{2}}\]. So here the nitrogen gas is formed.
When \[KN{{O}_{3}}\] is heated it gives potassium nitrite and oxygen. We can observe this by the following equation,
\[2KN{{O}_{3}}\to 2KN{{O}_{2}}+{{O}_{2}}\]. So here nitrogen gas is not evolved.
When \[{{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}(s)\] is heated it gives chromium oxide, nitrogen gas and water molecules. We can observe this by the following equation,
\[{{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}(s)\to C{{r}_{2}}{{O}_{3}}+{{N}_{2}}+4{{H}_{2}}O\].here nitrogen gas is evolved.
When \[N{{H}_{4}}N{{O}_{2}}(s)\] is heated it produces nitrogen gas and water as products. We can observe this by the following equation,
\[N{{H}_{4}}N{{O}_{2}}(s)\to {{N}_{2}}+2{{H}_{2}}O\]. Here nitrogen gas is evolved.
In industries nitrogen is widely produced in large volumes by cryogenic distillation. The small volumes of oxygen are produced by pressure swing adsorption method (PSA) or by diffusion separation processes. In the diffusion separation process the permeation is done through specially designed hollow fibers. Pure nitrogen is produced by the process called cryogenic distillation.

Hence the correct option for this question is option ‘b’.

Note: Nitrogen is widely used as a gas in manufacturing of fertilizers, nylon, nitric acid, etc. it is used in pharmaceutical industries in pharmaceutical drugs. It is also used to preserve sperm, egg, and blood. It is also used for shrinking the fittings so that they can be easily inserted. It is used as liquid in tunnel creation projects and excavating projects.