In a classical picture, nuclei can be understood as hard spheres that repel each other through the Coulomb force but fuse once the two spheres come close enough for contact. Estimating the radius of an atomic nuclei as about one femtometer, the energy needed for fusion of two hydrogen is:
This would imply that for the core of the sun, which has a Boltzmann distribution with a temperature of around 1.4 keV, the probability hydrogen would reach the threshold is , that is, fusion would never occur. However, fusion in the sun does occur due to quantum mechanics.