1. Identify the nature of each oxide

We need the oxide that shows magnetic property. In general, compounds containing ions with unpaired electrons show magnetic behavior (usually paramagnetism or ferrimagnetism).

2. Check each option

Option A: $MgO$

• Magnesium in $MgO$ is $Mg^{2+}$.
• Electronic configuration of $Mg$: $[Ne]3s^2$
• So, $Mg^{2+}$ has configuration $[Ne]$.
• No unpaired electrons rightarrow diamagnetic.

Option B: $SiO_2$

• $SiO_2$ is a covalent oxide.
• It does not contain partially filled $d$-orbitals or unpaired electrons responsible for magnetism.
• Hence, diamagnetic.

Option C: $Mn_3O_4$

• This is a mixed oxide: $MnO \cdot Mn_2O_3$.
• It contains both $Mn^{2+}$ and $Mn^{3+}$ ions.
• $Mn^{2+}$: $3d^5$ rightarrow unpaired electrons present.
• $Mn^{3+}$: $3d^4$ rightarrow unpaired electrons present.
• Therefore, $Mn_3O_4$ shows magnetic property.

Option D: $Na_2O$

• Sodium in $Na_2O$ is $Na^+$.
• Electronic configuration of $Na^+$ is $[Ne]$.
• No unpaired electrons rightarrow diamagnetic.

3. Conclusion

Among the given oxides, only $Mn_3O_4$ contains transition metal ions with unpaired electrons, so it shows magnetic property.

$\boxed{\text{Option C: } Mn_3O_4}$

4. Comparison with stored correct answer

• Derived answer: $C$
• Stored correct answer: $C$
• Therefore, they agree.