AgF, AgCl, NaCl, NaBr and NaI are colourless but AgBr and AgI are coloured because

Ag⁺ polarizes Br⁻ and I⁻ and not able to polarize Cl⁻ and F⁻

The correct answer is option 1.  Ag⁺ polarizes Br⁻ and I⁻ and not able to polarize Cl⁻ and F⁻.

The color of AgBr and AgI compared to the colorlessness of AgF, AgCl, NaCl, NaBr, and NaI can be explained primarily by the polarization effect of Ag\(^+\) ions on Br\(^-\) and I\(^-\) ions. 

Explanation:

Polarization Effect:

The polarization effect refers to the ability of a cation to distort the electron cloud of an anion. This distortion is significant in creating color in compounds. Ag\(^+\) is a relatively small and highly charged cation, which gives it a high polarizing power. Br\(^-\) and I\(^-\) are larger and more polarizable anions compared to Cl\(^-\) and F\(^-\). When Ag\(^+\) ions are in contact with Br\(^-\) or I\(^-\) ions, the significant polarization of the electron clouds of Br\(^-\) and I\(^-\) leads to changes in the electronic structure that result in the absorption of certain wavelengths of light, which manifests as color.

Lack of Polarization with Cl\(^-\) and F\(^-\):

Cl\(^-\) and F\(^-\) are smaller and less polarizable than Br\(^-\) and I\(^-\). The polarization by Ag\(^+\) on Cl\(^-\) and F\(^-\) is much weaker, resulting in no significant changes in electronic structure that would absorb visible light. Therefore, compounds like AgCl, NaCl, and NaF remain colorless.

Incorrect Options:

1. AgBr has unpaired electrons: This is not a primary factor for the color. The color in silver halides is more related to the polarizability and the resulting electronic transitions rather than unpaired electrons.

3. AgBr has defects: While defects can sometimes contribute to color, the primary reason for the color in AgBr and AgI is the polarization effect by Ag\(^+\).

4. All of these: This option is incorrect because the primary reason for the color difference is the polarization effect. The presence of unpaired electrons or defects is not the main cause in this context.

Conclusion: The main reason AgBr and AgI are colored while AgF, AgCl, NaCl, NaBr, and NaI are colorless is because Ag\(^+\) polarizes Br\(^-\) and I\(^-\) significantly, but is not able to similarly polarize Cl\(^-\) and F\(^-\). This polarization leads to changes in electronic structure and the absorption of visible light, resulting in color.