When ${\left({\text{NH}}_4\right)}_2{\text{Cr}}_2{\text{O}}_7$ is heated, the green coloured residue is:

The given reactant is ammonium dichromate${\left({\text{NH}}_4\right)}_2{\text{Cr}}_2{\text{O}}_7$. Ammonium dichromate is bright orange to red crystalline (sand-like) odorless solid. It is used in textile dyeing, as a pigment and oxidizing agent, and in the treatment of metals.

When ammonium dichromate is heated, it decomposes which means it breaks down to form smaller substances.

Thus, when ammonium dichromate is heated, it forms water vapors, nitrogen gas (gaseous due to the reaction temperature), with an orange spark, and solid chromium oxide.

The reaction can be written as follows:

$\left({\mathrm{NH}}_4\right)2{\mathrm{Cr}}_2{\mathrm{O}}_7\left(\mathrm{s}\right)\to {\mathrm{Cr}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+{\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

This solid chromium oxide obtained can be seen as a green residue at the bottom of the reaction container.

Hence, the correct option is (B).