(a) Calculate the transmission probability of an alpha particle of energy E = 5.0 MeV through a Coulomb barrier of a heavy nucleus that is approximated by a square barrier with V_0= 15 MeV and barrier width L=1.3 times 10^-14 m. Also, calculate the probability (b) by doubling the potential barrier height and (c) by using the original barrier height but doubling the barrier width. Compare all three probabilities.