In order to prepare a 1º amine from an alkyl halide with simultaneous addition of one CH₂ group in the carbon chain, the reagent used as source of nitrogen is-

Potassium cyanide 

The correct answer is option 3. Potassium cyanide.

Let us delve into the process of converting an alkyl halide to a primary amine with the simultaneous addition of one carbon atom using potassium cyanide \((KCN)\):

Step 1: Formation of the Nitrile

Reaction of Alkyl Halide with Potassium Cyanide:

Alkyl halides \((RCH_2X)\) react with potassium cyanide \((KCN)\) to form an alkyl nitrile \((RCH_2CN)\). The cyanide ion \((CN^−)\) is a nucleophile that substitutes the halide ion \((X^−)\) in the alkyl halide.

Here, \( R \) is the alkyl group, \( X \) is the halide (e.g., \(Cl, Br, I\)), and \( CN \) is the cyanide group.

Step 2: Reduction of the Nitrile

Reduction of Nitrile to Primary Amine:

The nitrile group \((RCH_2CN)\) can be reduced to a primary amine \((RCH_2CH_2NH_2)\). Common reducing agents for this process include hydrogen in the presence of a catalyst (such as Raney nickel), or using reducing agents like lithium aluminum hydride \((LiAlH_4)\).

This reduction adds an additional \( CH_2 \) group to the carbon chain, converting the nitrile group (-CN) to an amine group \((-NH_2)\).

Example: Let us go through a specific example:

Starting Material: Bromoethane \((CH_3CH_2Br)\)

1. Formation of Propionitrile:

Here, bromoethane (ethyl bromide) reacts with potassium cyanide to form propionitrile (ethyl cyanide).

2. Reduction to Propylamine:

Propionitrile is then reduced to propylamine, adding one \( CH_2 \) group to the chain.

Summary

Reacting the alkyl halide \((RCH_2X)\) with potassium cyanide \((KCN)\) forms an alkyl nitrile \((RCH_2CN)\). Reducing the nitrile \((RCH_2CN)\) forms a primary amine \((RCH_2CH_2NH_2)\) with the addition of one carbon atom.

Thus, potassium cyanide is used as the source of nitrogen and facilitates the addition of one \( CH_2 \) group to the carbon chain, effectively converting the alkyl halide into a primary amine. The correct answer is therefore: Potassium cyanide.