Step 1: Understanding nucleophilic substitution.
In nucleophilic substitution reactions (SN1 and SN2), when a nucleophile like CN\(^-\) attacks a chiral carbon, the configuration of the carbon can invert in the case of an SN2 reaction. For \( (R)-2-bromobutane \), the CN\(^-\) will attack the electrophilic carbon, leading to inversion of configuration.
Step 2: Analyzing the options.
(A) retention of configuration: Incorrect — Retention of configuration is characteristic of SN1 reactions, not SN2.
(B) inversion of configuration: Correct — The CN\(^-\) nucleophile will cause inversion of configuration in this SN2 reaction.
(C) formation of CH\(_3\)-CH(CH\(_2\))CH\(_2\): Incorrect — This is a product that does not match the reaction.
(D) formation of (S)-2-methylbutanenitrile: Incorrect — The product is correct in terms of structure but does not match the configuration change (inversion is expected).
Step 3: Conclusion.
The correct answer is (B) inversion of configuration, as the reaction proceeds by an SN2 mechanism, causing inversion of configuration.