A law of small numbers for a mutation process

A system of particles will consist of 2n particles at time n, n = 0,1,2,...; each of the particles is either blue or white. At time 0 the particle is white. In the time interval (0,1) this particle mutates to blue with probability p. At time 1 the particle splits into two particles of the same color. At any time n greater than or equal to 1 the 2n particles act independently of each other and of their ancestral histories; during the time interval (n, n + 1) each white particle mutates to blue with probability p, and each blue particle mutates to white with probability alpha. The problem is to find the distribution of the number, Xn, of blue particles at time n - 0 when n is large and p = pn and alpha = alpha n are small.