Why in a three pin plug the earth pin is thicker and longer than the other pins?

It depends upon R=rho l/a where area(a) is inversely proportional to resistance (R), so if (a) increases, R decreases & if R is less the leakage current will take low resistance path so the earth pin should be thicker. It is longer  because the First to make the connection and last to disconnect should be earth Pin. This assures Safety for the person who uses the electrical instrument.