▶ An electron at rest is released far away from a proton, toward which it moves. 

(a) Show that the de Broglie wavelength of the electron is proportional to square root for r, where r is the distance of the electron from the proton. 

(b) Find the wavelength of the electron when it is a0 from the proton. How does this compare with the wavelength of an electron in a ground-state Bohr orbit? 

(c) In order for the electron to be captured by the proton to form a ground-state hydrogen atom, energy must be lost by the system. How much energy?