Step 1: Understand the nature of AlCl\(_3\).
AlCl\(_3\) is a covalent compound in the vapour phase and exists as a monomer at high temperature. However, in order to attain stability, it tends to form a dimer Al\(_2\)Cl\(_6\). This is due to electron deficiency of aluminium.
Step 2: Reason for dimer formation.
Aluminium in AlCl\(_3\) has only 6 electrons in its valence shell, making it electron deficient. To complete its octet, it accepts electron pairs from chlorine atoms of another AlCl\(_3\) molecule, forming coordinate bonds and a bridged dimer structure Al\(_2\)Cl\(_6\).
Step 3: Evaluation of Assertion (A).
Since dimerization reduces electron deficiency and increases stability through bridging chlorine atoms and coordinate bonding, the assertion that AlCl\(_3\) becomes stable by forming a dimer is correct.
Step 4: Evaluation of Reason (R).
The reason states that aluminium cannot accept electrons from bridging chlorine atoms. This statement is incorrect because in reality Al accepts lone pair electrons from chlorine atoms to form coordinate bonds in Al\(_2\)Cl\(_6\).
Step 5: Bonding in Al\(_2\)Cl\(_6\).
In the dimer, two chlorine atoms act as bridges between two aluminium atoms. Each bridge involves donation of lone pair from chlorine to electron-deficient aluminium, forming dative bonds. This clearly shows aluminium does accept electron density.
Step 6: Final conclusion.
Therefore, Assertion (A) is true, but Reason (R) is false. Hence, R does not explain A.
Final Answer:
\[
\boxed{(3)}
\]