bas two elec and one in the 2s. Consider an excited state in which the ostermost clectron has be a fairly ne calculation of an ac- ation p(r) is very hard, but it is easy to been raised to the 3p level. Since the 3p wave func make a fairly realistic guess. For example, one might guess that p(r) is spherically symmetric and given by tions are not very penetrating-you energy of this electron by etimate the eg it is completely outside both the other electrons. (a) In this approti- mation what is the potential p(r) = y fusctic felt by the outermost clectron? (b) In the same appr Poe r/R where R is some sort of mean atomic radius. (a) Given that p(r) is the average charge distribution of Z - 1 electrons, find po in terms of Z, e, and R. (b) Use Gauss's law to find the electric field& at a point r due to the nucleus and the charge distribution p. (c) Verify that as r→0 and r-0, & behaves as required by (10.2) and (10.3). [Hint: The integrals needed in parts (a) and (b) are in Appendix B. tion write the formula for the energy of the outer electron if its principal tam number (c) Estimate the energy of the 3p clectoon of electron is ia the 3d level, whose observed energy is -1513e (e) Explain why the agreement is better for the level than for the 3p. Why is the obsen and compare with the observed val (d) Repeat for the case that the ou us and the rons 3p lower than that for 3d? SECTION 10.4 (The Pauli Exclusion Principle) (a) How many electrons can be accommodate an electron energy level with / 22 (b) How ma 1= 3? (c) Give a formula (in term ber of electrons that can be accom with arbitrary L SECTION 10.3 (The IPA Energy Levels) 10.7 10.3 (a) Estimate the energy of the innermost electron of lead. (b) What is its most probable radius? (Appendix C has a list of atomic numbers.) the m state 10.8 (a) Imagine an electron (spins= confina one-dimensional rigid box. What are the des cies of its energy levels? (b) Make a sketch lowest few levels, showing their occupancy lowest state of six electrons confined in box. (Ignore the Coulomb repulsion an electrons). 10.4 Answer the same questions as in Problem 10.3, but for silver. ons 10.5 The ground state of sodium (Z = 11) has two electrons in the 1s level, two in the 2s, six in the 2p, and one in the 3s. Consider an excited state in which functions the nutermost electron has been raised to a 3d state nchanged), Because trons

bas two elec and one in the 2s. Consider an excited state in which the ostermost clectron has be a fairly ne calculation of an ac- ation p(r) is very hard, but it is easy to been raised to the 3p level. Since the 3p wave func make a fairly realistic guess. For example, one might guess that p(r) is spherically symmetric and given by tions are not very penetrating-you energy of this electron by etimate the eg it is completely outside both the other electrons. (a) In this approti- mation what is the potential p(r) = y fusctic felt by the outermost clectron? (b) In the same appr Poe r/R where R is some sort of mean atomic radius. (a) Given that p(r) is the average charge distribution of Z - 1 electrons, find po in terms of Z, e, and R. (b) Use Gauss's law to find the electric field& at a point r due to the nucleus and the charge distribution p. (c) Verify that as r→0 and r-0, & behaves as required by (10.2) and (10.3). [Hint: The integrals needed in parts (a) and (b) are in Appendix B. tion write the formula for the energy of the outer electron if its principal tam number (c) Estimate the energy of the 3p clectoon of electron is ia the 3d level, whose observed energy is -1513e (e) Explain why the agreement is better for the level than for the 3p. Why is the obsen and compare with the observed val (d) Repeat for the case that the ou us and the rons 3p lower than that for 3d? SECTION 10.4 (The Pauli Exclusion Principle) (a) How many electrons can be accommodate an electron energy level with / 22 (b) How ma 1= 3? (c) Give a formula (in term ber of electrons that can be accom with arbitrary L SECTION 10.3 (The IPA Energy Levels) 10.7 10.3 (a) Estimate the energy of the innermost electron of lead. (b) What is its most probable radius? (Appendix C has a list of atomic numbers.) the m state 10.8 (a) Imagine an electron (spins= confina one-dimensional rigid box. What are the des cies of its energy levels? (b) Make a sketch lowest few levels, showing their occupancy lowest state of six electrons confined in box. (Ignore the Coulomb repulsion an electrons). 10.4 Answer the same questions as in Problem 10.3, but for silver. ons 10.5 The ground state of sodium (Z = 11) has two electrons in the 1s level, two in the 2s, six in the 2p, and one in the 3s. Consider an excited state in which functions the nutermost electron has been raised to a 3d state nchanged), Because trons