We need to identify which compound gives nitrogen gas, $N_2$, on thermal decomposition.

Check each option:

A. $Ba(NO_3)_2$

Barium nitrate is a nitrate of an alkaline earth metal. On heating, such nitrates generally decompose to oxide, nitrogen dioxide, and oxygen: $2Ba(NO_3)_2 \rightarrow 2BaO + 4NO_2 + O_2$ This does not produce $N_2$ gas.

B. $Ba(N_3)_2$

Here $N_3^-$ is the azide ion. Metal azides decompose on heating to give the metal and nitrogen gas: $Ba(N_3)_2 \rightarrow Ba + 3N_2$ So this option does produce $N_2$ gas.

C. $NaNO_2$

Sodium nitrite on heating decomposes as: $2NaNO_2 \rightarrow Na_2O + NO + NO_2$ It does not give nitrogen gas as the main product.

D. $NaNO_3$

Alkali metal nitrates (except lithium nitrate) decompose to nitrites and oxygen: $2NaNO_3 \rightarrow 2NaNO_2 + O_2$ No $N_2$ is formed.

Therefore, the compound that gives nitrogen gas on heating is: $\boxed{Ba(N_3)_2}$

Comparing with the stored correct answer:

• Derived answer: B
• Stored correct answer: B
• They match.