Physics question 11 hw 20

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Find the energy of the electron in the ground state of doubly inozed lithium, which has an atomic number Z = 3. Answer in units of eV.

Find the radius of its ground-state orbit. Answer in units of nm.

Jul 14th, 2015

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(a) To get the result for doubly ionized lithium, replace e2 by Ze2 in the expression for the energy levels.
En = (me ke2 Z2 e4 / 2 hbar2) (1/n2) = -Z2 (13.6eV / n2) = -122.4eV / n2
The ground state energy is
E1 = -122.4eV

(b) Make the same change to the expression for the radius:
rn = n2 hbar2 / me ke Z e2 = n2 a0 / Z
The ground-state radius is
r1 = a0 / Z = 0.0529nm / 3 = 0.0176nm

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 14th, 2015

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