1. Let the masses be $m_1 = 4\,\text{g}, \qquad m_2 = 16\,\text{g}$

2. Given that both particles have equal kinetic energies.

   Using the relation between kinetic energy and momentum, $K = \frac{p^2}{2m}$

   Since kinetic energies are equal, $\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$

3. Substitute the masses: $\frac{p_1^2}{2\cdot 4} = \frac{p_2^2}{2\cdot 16}$

   The factor of 2 cancels: $\frac{p_1^2}{4} = \frac{p_2^2}{16}$

4. Cross-multiply: $16p_1^2 = 4p_2^2$ $4p_1^2 = p_2^2$

   Taking square root, $p_2 = 2p_1$

   So, $p_1 : p_2 = 1 : 2$

5. The ratio is given as $n : 2$ Comparing, $n = 1$

Final Answer

$\boxed{1}$