The ground state wavefunction of the electron in the hydrogen atom is spherically symmetric which means that the wavefunction phi (r) can be written solely in terms of the radial coordinate r representing the distance between the proton and electron. (a) What does the quantity | phi (r)|^2 mean physically? (b) Show that the volume of a thin spherical shell of radius r and thickness dr is 4 pi r^2 dr. (You can use the approximation for small dr that the volume is the surface area of the sphere times dr.) (c) In spherical coordinates, the ground state solution of the Schrodinger equation for the hydrogen atom is phi_100 = 1/Squareroot pi a_0^3 e^-r/a_0, where a_0 is the same constant as from the previous problem. Use the result of part (b) to write an expression for the probability that the electron is in a spherical shell of radius r and thickness dr. (d) Calculate the radius of the shell (of constant thickness dr) where the electron is most likely to be found.