Solution:

The internal energy \( U \) of an ideal gas is given by:

\[
U = n \cdot C_V \cdot T
\]

For a diatomic gas like hydrogen (\( \text{H}_2 \)), \( C_V = \frac{5}{2} R \), and for a monoatomic gas like helium (\( \text{He} \)), \( C_V = \frac{3}{2} R \).

Given that the internal energy of \( n_1 \) moles of hydrogen at temperature \( T \) is equal to the internal energy of \( n_2 \) moles of helium at temperature \( 2T \), we have:

\[
n_1 \cdot \frac{5}{2} R \cdot T = n_2 \cdot \frac{3}{2} R \cdot (2T)
\]

Simplifying:

\[
\frac{5}{2} n_1 = 3 n_2
\]

Rearrange to find the ratio \( \frac{n_1}{n_2} \):

\[
\frac{n_1}{n_2} = \frac{3}{5} \cdot \frac{2}{1} = \frac{6}{5}
\]

Answer: The ratio \( \frac{n_1}{n_2} \) is \( \frac{6}{5} \).