`(NH_4)_2Cr_2O_7` on heating gives a gas which is also given by

Options

A. heating `NH_4NO_2`
B. Heating `NH_4NO_3`
C. `Mg_3N_2+H_2O`
D. `Na+H_2O_2`

Explanation

To solve the question, we need to determine the gas produced when ammonium dichromate \((NH_4)_2Cr_2O_7\) is heated, and then identify which of the given compounds also produces the same gas.

### Step-by-Step Solution:

1. **Identify the Reaction of Ammonium Dichromate**:
When ammonium dichromate \((NH_4)_2Cr_2O_7\) is heated, it decomposes to form chromium(III) oxide \((Cr_2O_3)\), water \((H_2O)\), and nitrogen gas \((N_2)\). The balanced equation for this reaction is:
\[ (NH_4)_2Cr_2O_7 \rightarrow Cr_2O_3 + 4H_2O + N_2 \]
Thus, the gas produced is nitrogen gas \((N_2)\).

2. **Evaluate Each Given Compound**:
We need to check each of the provided compounds to see if they also produce nitrogen gas when heated.

- **Option 1: Ammonium Nitrite \((NH_4NO_2)\)**:
\[ NH_4NO_2 \rightarrow 2H_2O + N_2 \]
This reaction produces nitrogen gas \((N_2)\).

- **Option 2: Ammonium Nitrate \((NH_4NO_3)\)**:
\[ NH_4NO_3 \rightarrow N_2O + 2H_2O \]
This reaction produces nitrous oxide \((N_2O)\), not nitrogen gas \((N_2)\).

- **Option 3: Magnesium Nitride \((Mg_3N_2)\) with Water**:
\[ Mg_3N_2 + 6H_2O \rightarrow 3Mg(OH)_2 + N_2 \]
This reaction produces nitrogen gas \((N_2)\).

- **Option 4: Sodium with Hydrogen Peroxide \((Na + H_2O_2)\)**:
This reaction does not involve nitrogen, and therefore cannot produce nitrogen gas \((N_2)\).

3. **Conclusion**:
From the evaluation, the compounds that produce nitrogen gas \((N_2)\) are:
- Ammonium Nitrite \((NH_4NO_2)\)
- Magnesium Nitride \((Mg_3N_2)\)

However, since the question asks for a single answer, the most direct answer from the options provided is **Option 1: Ammonium Nitrite \((NH_4NO_2)\)**.

### Final Answer:
The gas produced by \((NH_4)_2Cr_2O_7\) on heating is nitrogen gas \((N_2)\), which is also produced by **Option 1: Ammonium Nitrite \((NH_4NO_2)\)**.