Step 1: Understanding the stoichiometry.
The hydrogenation of ethene (\( C_2H_4 \)) follows the reaction:
\[
C_2H_4 + H_2 \rightarrow C_2H_6
\]
For every 1 mole of ethene, 1 mole of hydrogen is required. Since the volume of gases at S.T.P. is directly proportional to the number of moles, the volume of hydrogen required is equal to the volume of ethene.
Step 2: Conclusion.
The correct answer is (B) \( 0.5 \, \text{dm}^3 \).