In this problem we will learn why quantum tunnelling plays a role in nuclear fusion. i) The Sun has an internal temperature of T ~ 107K. How much kinetic energy does a proton inside the sun have? (2) ii) Fusion in the Sun occurs when protons collide. However, they must overcome a potential barrier 4 MeV high and ~ 5 X 10'14m wide. Considering the solution to the previous questions, this is obviously not possible classically. Calculate the quantum tunnelling likelihood. (1) iii) Two protons collide every 10113. How long on average until they undergo fusion? Discuss the physical consequence of this. (2)