PH 253 Midterm: ph253_F13_Exam_3
Document Summary
All problems have equal weight: a long time ago, in a galaxy far, far away, electric charge had not yet been invented, and atoms were held together by gravitational forces. Find the equivalent of the bohr radius for a gravita- tionally bound atom symbolically, and then make a numerical estimate. Note that the bohr radius for an electrically-bound atom is ao = 4 o2/mee2. You should be able to nd the correct result by comparing the electric and gravitational potential energies below and making the appropriate substitutions. Gmpme r (1) here me is the electron mass, mp the proton mass, and g = 6. 67 10 11 n m2/kg2 is the gravitational constant. Dimensional analysis may be a good double check: energetics of diatomic systems an expression for the potential energy of two neutral atoms as a function of their separation r is given by the morse potential, Note: equilibrium is characterized by du/dr = 0.
