The question requires identifying the grammatically correct sentence among the given options, focusing on the usage of negative adverbs like 'hardly' and 'scarcely'.

Grammar Rule for Hardly and Scarcely

When 'hardly' or 'scarcely' start a sentence, they trigger an inversion, meaning the auxiliary verb comes before the subject. The correct conjunction to follow these adverbs in such constructions is typically 'when' or 'before'.

• Structure: Hardly/Scarcely + auxiliary verb + subject + main verb + ... when/before + second clause.

Analysis of Options

Option (a): Hardly had I arrived at the airport than the plane departed.

This sentence uses the correct inversion ('Hardly had I arrived'). However, it incorrectly uses 'than' as the conjunction. 'Hardly' should be followed by 'when' or 'before'.

Option (b): Scarcely had I arrived at the airport when the plane departed.

This sentence correctly employs inversion ('Scarcely had I arrived') and uses the appropriate conjunction 'when'. This structure follows the standard rule for 'scarcely'.

Option (c): Hardly I had arrived at the airport when the plane departed.

This sentence is incorrect because it fails to use inversion. When 'hardly' starts a sentence, the auxiliary verb ('had') must precede the subject ('I'). The structure should be 'Hardly had I...'.

Option (d): Scarcely had I arrived at the airport then the plane departed.

This sentence uses the correct inversion ('Scarcely had I arrived'). However, it incorrectly uses 'then' as the conjunction. 'Scarcely' requires 'when' or 'before' to connect the two clauses.

Conclusion

Based on the grammatical rules for negative adverbs and conjunctions, sentence (b) is the only correctly formed sentence.