Question

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a) First, the Coulomb force is the centripetal force; set the two expressions equal to each other and solve for mv.

b) Secondly, the angular momentum of the orbiting electron is quantized. Set the expression for the classical angular momentum equal 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 = the electric potential energy (use the approach from part a). Then use your expression (not the value) for r in part b to write the remaining (½)U in terms of 1/n2.

e) Calculate a value for the coefficient of 1/n2 in the expression from the previous part.

f) That expression is the ionization energy in terms of the quantum number n. Write the difference in energy levels (the energy of the photon emitted) in terms of h,c and λ, set it equal to the expression in (e) and rearrange to get the same form as Rydberg’s equation.

g) Calculate the coefficient in front of the difference in 1/λ and compare to Rydberg’s constant.

ONLY DO d THROUGH g! Thank you!

Answer 1