bas two elecand one in the 2s. Consider anexcited state in which the ostermost clectron hasbe a fairlyne calculation of an ac-ation p(r) is very hard, but it is easy tobeen raised to the 3p level. Since the 3p wave funcmake a fairly realistic guess. For example, one mightguess that p(r) is spherically symmetric and given bytions are not very penetrating-youenergy of this electron byetimate theeg it is completelyoutside both the other electrons. (a) In this approti-mation what is the potentialp(r) =y fuscticfelt bythe outermost clectron? (b) In the same apprPoe r/Rwhere R is some sort of mean atomic radius.(a) Given that p(r) is the average charge distributionof Z - 1 electrons, find po in terms of Z, e, and R.(b) Use Gauss's law to find the electric field& at apoint r due to the nucleus and the charge distributionp. (c) Verify that as r→0 and r-0, & behaves asrequired by (10.2) and (10.3). [Hint: The integralsneeded in parts (a) and (b) are in Appendix B.tion write the formula for the energy of the outerelectron if its principaltam number(c) Estimate the energy of the 3p clectoonofelectron is iathe 3d level, whose observed energy is -1513e(e) Explain why the agreement is better for thelevel than for the 3p. Why is the obsenandcompare with the observed val(d) Repeat for the case that the ouus and therons3p lower than that for 3d?SECTION 10.4 (The Pauli Exclusion Principle)(a) How many electrons can be accommodatean electron energy level with / 22 (b) How ma1= 3? (c) Give a formula (in termber of electrons that can be accomwith arbitrary LSECTION 10.3 (The IPA Energy Levels)10.710.3 (a) Estimate the energy of the innermost electronof lead. (b) What is its most probable radius?(Appendix C has a list of atomic numbers.)them state10.8 (a) Imagine an electron (spins= confinaone-dimensional rigid box. What are the descies of its energy levels? (b) Make a sketchlowest few levels, showing their occupancylowest state of six electrons confined inbox. (Ignore the Coulomb repulsion anelectrons).10.4 Answer the same questions as in Problem 10.3, butfor silver.ons10.5 The ground state of sodium (Z = 11) has twoelectrons in the 1s level, two in the 2s, six in the 2p,and one in the 3s. Consider an excited state in whichfunctionsthe nutermost electron has been raised to a 3d statenchanged), Becausetrons

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Asked Dec 3, 2019
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How might I appropriately answer 10.3?

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
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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

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Expert Answer

Step 1

(a) Energy of the inner most electron of lead is,

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z2 E (13.6eV) n (82) -(13.6 eV) E (1) = -91446.4 eV N-91.45keV

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Step 2

(b) Most probable ...

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Z (1)* a 82 52.9pm 82 0.645 pm

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