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a) First, the Coulomb force is the centripetal force; set thetwo expressions equal to each other and solve for mv.
b) Secondly, the angular momentum of the orbiting electron isquantized. Set the expression for the classical angular momentumequal to nħ and solve the resulting equation for r.
c) For n=1, determine the orbital radius r. q=e=-1.6 x 10-19 [C]ħ=1.055x10-34 [Js] ke=9x109 [Nm2/C2] me=9.09x10-31[kg]
d) Show that the kinetic energy = -(1/2) U, where U = theelectric potential energy (use the approach from part a). Then useyour expression (not the value) for r in part b to write theremaining (½)U in terms of 1/n2.
e) Calculate a value for the coefficient of 1/n2 in theexpression from the previous part.
f) That expression is the ionization energy in terms of thequantum number n. Write the difference in energy levels (the energyof the photon emitted) in terms of h,c and λ, set it equal to theexpression in (e) and rearrange to get the same form as Rydberg’sequation.
g) Calculate the coefficient in front of the difference in 1/λand compare to Rydberg’s constant.
ONLY DO d THROUGH g! Thank you!
