ing periOptical excitationsvalence electronX-таy excitationsinner electronsPROBLEMS FOR CHAPTER 10g. 10.17.v line ofSECTION 10.2 (The Independent-Particlethe 3d wave function is not verytreat the outer electron as if itside all the other electrons. (a)what is the potential-energy furouter electron? (b) In the sameshould be the energy of an elCompare your answer with t-1.52 eV. Why is the observedestimate?Approximation)ectrum10.1 Find the electric field & at r = ag in the 1s state ofa hydrogen atom. Compare with the breakdown fieldof dry air, about 3 x 10° V/m. [Hint: Use Gauss'slaw; treat the atomic electron as a static charge distri-bution with charge density p(r) = -e(r)P and usethe result of Problem 8.43.]10.2 The IPA potential-energy function U(r) is thepotential energy "felt" by an atomic electron in theaverage field of the other Z - 1 electrons plus thenucleus. If one knew the average charge distributionP r) of the Z - 1 other electrons, it would be a fairlysimple matter to find U(r). The calculation of an ac-curate distribution p(r) is very hard, but it is easy to10.6 The ground state of lithiumtrons in the 1s level and oneexcited state in which the obeen raised to the 3p level. Sitions are not very penetratingenergy of this electron byoutside both the other electromation what is the potential-ahtmol Chapter 8 The Three-Dimensional Schrödinger Equation2868.50 Write down the radial densit2p states of hydrogen. [See (8the most probable radius forHint: If P(r) is maximum, so8.42 ** 7he average (or expectation) value (r) of theradius for any state isrP(r) dr. Find (r) for the 1sstate of hydrogen. Referring to Fig. 8.18, explain thedifference between the average and most probableradii.8.43 ** The probability of finding the electron in theregion r > a is P(r) dr. What is the probabilitythat a 1s electron in hydrogen would be found out-side the Bohr radius (r > ag)?SECTION 8.10 (Hydrogen-LikeWhat is the most probable8.51the hydrogen-like ion Ni2v8.44 (a) Write down the radial equation (8.107) for thecase that n 2 and / 0 and verify that8.52 An inner electron in a hetively little by the other ewave function very like thorbit around the samewhat is the most probablelead? What is this electenergy?= A 2-R2sis a solution. (b) Use the normalization condition(8.86) to find the constant A. (See Appendix B.)Write down the radial equation (8.72) for the case8 45 #*A hydrogen-like ion M8.53

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How might I appropriately answer 10.1?

ing peri
Optical excitations
valence electron
X-таy excitations
inner electrons
PROBLEMS FOR CHAPTER 10
g. 10.17.
v line of
SECTION 10.2 (The Independent-Particle
the 3d wave function is not very
treat the outer electron as if it
side all the other electrons. (a)
what is the potential-energy fur
outer electron? (b) In the same
should be the energy of an el
Compare your answer with t
-1.52 eV. Why is the observed
estimate?
Approximation)
ectrum
10.1 Find the electric field & at r = ag in the 1s state of
a hydrogen atom. Compare with the breakdown field
of dry air, about 3 x 10° V/m. [Hint: Use Gauss's
law; treat the atomic electron as a static charge distri-
bution with charge density p(r) = -e(r)P and use
the result of Problem 8.43.]
10.2 The IPA potential-energy function U(r) is the
potential energy "felt" by an atomic electron in the
average field of the other Z - 1 electrons plus the
nucleus. If one knew the average charge distribution
P r) of the Z - 1 other electrons, it would be a fairly
simple matter to find U(r). The calculation of an ac-
curate distribution p(r) is very hard, but it is easy to
10.6 The ground state of lithium
trons in the 1s level and one
excited state in which the o
been raised to the 3p level. Si
tions are not very penetrating
energy of this electron by
outside both the other electro
mation what is the potential-
aht
mol
help_outline

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ing peri Optical excitations valence electron X-таy excitations inner electrons PROBLEMS FOR CHAPTER 10 g. 10.17. v line of SECTION 10.2 (The Independent-Particle the 3d wave function is not very treat the outer electron as if it side all the other electrons. (a) what is the potential-energy fur outer electron? (b) In the same should be the energy of an el Compare your answer with t -1.52 eV. Why is the observed estimate? Approximation) ectrum 10.1 Find the electric field & at r = ag in the 1s state of a hydrogen atom. Compare with the breakdown field of dry air, about 3 x 10° V/m. [Hint: Use Gauss's law; treat the atomic electron as a static charge distri- bution with charge density p(r) = -e(r)P and use the result of Problem 8.43.] 10.2 The IPA potential-energy function U(r) is the potential energy "felt" by an atomic electron in the average field of the other Z - 1 electrons plus the nucleus. If one knew the average charge distribution P r) of the Z - 1 other electrons, it would be a fairly simple matter to find U(r). The calculation of an ac- curate distribution p(r) is very hard, but it is easy to 10.6 The ground state of lithium trons in the 1s level and one excited state in which the o been raised to the 3p level. Si tions are not very penetrating energy of this electron by outside both the other electro mation what is the potential- aht mol

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Chapter 8 The Three-Dimensional Schrödinger Equation
286
8.50 Write down the radial densit
2p states of hydrogen. [See (8
the most probable radius for
Hint: If P(r) is maximum, so
8.42 ** 7he average (or expectation) value (r) of the
radius for any state isrP(r) dr. Find (r) for the 1s
state of hydrogen. Referring to Fig. 8.18, explain the
difference between the average and most probable
radii.
8.43 ** The probability of finding the electron in the
region r > a is P(r) dr. What is the probability
that a 1s electron in hydrogen would be found out-
side the Bohr radius (r > ag)?
SECTION 8.10 (Hydrogen-Like
What is the most probable
8.51
the hydrogen-like ion Ni2v
8.44 (a) Write down the radial equation (8.107) for the
case that n 2 and / 0 and verify that
8.52 An inner electron in a he
tively little by the other e
wave function very like th
orbit around the same
what is the most probable
lead? What is this elect
energy?
= A 2-
R2s
is a solution. (b) Use the normalization condition
(8.86) to find the constant A. (See Appendix B.)
Write down the radial equation (8.72) for the case
8 45 #*
A hydrogen-like ion M
8.53
help_outline

Image Transcriptionclose

Chapter 8 The Three-Dimensional Schrödinger Equation 286 8.50 Write down the radial densit 2p states of hydrogen. [See (8 the most probable radius for Hint: If P(r) is maximum, so 8.42 ** 7he average (or expectation) value (r) of the radius for any state isrP(r) dr. Find (r) for the 1s state of hydrogen. Referring to Fig. 8.18, explain the difference between the average and most probable radii. 8.43 ** The probability of finding the electron in the region r > a is P(r) dr. What is the probability that a 1s electron in hydrogen would be found out- side the Bohr radius (r > ag)? SECTION 8.10 (Hydrogen-Like What is the most probable 8.51 the hydrogen-like ion Ni2v 8.44 (a) Write down the radial equation (8.107) for the case that n 2 and / 0 and verify that 8.52 An inner electron in a he tively little by the other e wave function very like th orbit around the same what is the most probable lead? What is this elect energy? = A 2- R2s is a solution. (b) Use the normalization condition (8.86) to find the constant A. (See Appendix B.) Write down the radial equation (8.72) for the case 8 45 #* A hydrogen-like ion M 8.53

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Expert Answer

Step 1

Write the expression for charge density

-еxp
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-еxp

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Step 2

Write the expression for electric field

pаY
Е-
4ле
(4лr*dr)
exp
4ле
ла
аз
в
dr
exp
Лаз
аз
е,
а
еxp(-2r/ a,)
(-2r/ ag)
ла,
е,
2e
( екp (-2) - скр (0))
4ле,ар
Ф
Il
II
help_outline

Image Transcriptionclose

pаY Е- 4ле (4лr*dr) exp 4ле ла аз в dr exp Лаз аз е, а еxp(-2r/ a,) (-2r/ ag) ла, е, 2e ( екp (-2) - скр (0)) 4ле,ар Ф Il II

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Step 3

Substitute the...

2(1.6x10-19 C)(9x10° Nm2 / C2 ,
(0.53x10-10 m)
(ехp(-2)- ехp (0))
=88.6x100 Vim
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2(1.6x10-19 C)(9x10° Nm2 / C2 , (0.53x10-10 m) (ехp(-2)- ехp (0)) =88.6x100 Vim

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