Question

can three atoms of carbon form a molecule of carbon

Answer 1

Three carbon atoms can be bound in such ways:

1) linear structure: $C = C = C$

2) Cyclic structure:

In the first structure, the two terminal carbon atoms have an incomplete octet. In the second structure the angle strain in cycle is extremely high (C-C-C angle is $60^{\circ}$ instead of normal $180^{\circ}$ for sp-hybridization). Therefore, the occurrence of such molecules is unfavourable.