If you are unsure how to find the polarizability of a metallic sphere, study the Problem 2 of IPhO-2013, parts 1 to 4.
Double-check all the numerical factors and check for possible mistakes with dimensions (non-matching units in expressions). It is very easy to overlook a factor of two, or something similar by this problem.
NB! The final deadline of the first problem is extended to 22nd December, 23:59 GMT. It will take few more days to get the final results of the Problem 1 published.