I am having trouble understanding why the excluded volume of a particle is four times its actual volume.
According to Wikipedia, "The excluded volume b is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times the total molecular volume for one mole of a Van der waals' gas. To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original radius) that is forbidden for the centers of the other particles. If the distance between two particle centers were to be smaller than 2r, it would mean that the two particles penetrate each other, which, by definition, hard spheres are unable to do."
I do understand that the centre of one particle will not be able to enter the sphere of radius 2r surrounding the other particle. But shouldn't atleast half the volume of the particle be able to enter the sphere?