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Determine the lowest three rotational energy levels of H 2 .

E 0 r = 7.43 × 10 −3 eV ; l = 0 ; E r = 0 eV (no rotation);
l = 1 ; E r = 1.49 × 10 −2 eV ; l = 2 ; E r = 4.46 × 10 −2 eV

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A carbon atom can hybridize in the s p 2 configuration. (a) What is the angle between the hybrid orbitals?

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List five main characteristics of ionic crystals that result from their high dissociation energy.

  1. They are fairly hard and stable.
  2. They vaporize at relatively high temperatures (1000 to 2000 K).
  3. They are transparent to visible radiation, because photons in the visible portion of the spectrum are not energetic enough to excite an electron from its ground state to an excited state.
  4. They are poor electrical conductors because they contain effectively no free electrons.
  5. They are usually soluble in water, because the water molecule has a large dipole moment whose electric field is strong enough to break the electrostatic bonds between the ions.
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Why is bonding in H 2 + favorable? Express your answer in terms of the symmetry of the electron wave function.

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Astronomers claim to find evidence of He 2 from light spectra of a distant star. Do you believe them?

No, He atoms do not contain valence electrons that can be shared in the formation of a chemical bond.

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Show that the moment of inertia of a diatomic molecule is I = μ r 0 2 , where μ is the reduced mass, and r 0 is the distance between the masses.

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Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by E = 1 2 E F .

1 N / 2 n 2 = 1 3 ( N 2 ) 3 , so E = 1 3 E F

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Measurements of a superconductor’s critical magnetic field (in T ) at various temperatures (in K) are given below. Use a line of best fit to determine B c ( 0 ) . Assume T c = 9.3 K .

T (in K) B c ( T )
3.0 0.18
4.0 0.16
5.0 0.14
6.0 0.12
7.0 0.09
8.0 0.05
9.0 0.01
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Estimate the fraction of Si atoms that must be replaced by As atoms in order to form an impurity band.

An impurity band will be formed when the density of the donor atoms is high enough that the orbits of the extra electrons overlap. We saw earlier that the orbital radius is about 50 Angstroms, so the maximum distance between the impurities for a band to form is 100 Angstroms. Thus if we use 1 Angstrom as the interatomic distance between the Si atoms, we find that 1 out of 100 atoms along a linear chain must be a donor atom. And in a three-dimensional crystal, roughly 1 out of 10 6 atoms must be replaced by a donor atom in order for an impurity band to form.

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Transition in the rotation spectrum are observed at ordinary room temperature ( T = 300 K ). According to your lab partner, a peak in the spectrum corresponds to a transition from the l = 4 to the l = 1 state. Is this possible? If so, determine the momentum of inertia of the molecule.

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Determine the Fermi energies for (a) Mg, (b) Na, and (c) Zn.

a. E F = 7.11 eV ; b. E F = 3.24 eV ; c. E F = 9.46 eV

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Find the average energy of an electron in a Zn wire.

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What value of the repulsion constant, n , gives the measured dissociation energy of 158 kcal/mol for CsCl?

9.15 9

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A physical model of a diamond suggests a BCC packing structure. Why is this not possible?

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Challenge problems

For an electron in a three-dimensional metal, show that the average energy is given by E = 1 N 0 E F E g ( E ) d E = 3 5 E F ,

Where N is the total number electrons in the metal.

In three dimensions, the energy of an electron is given by:
E = R 2 E 1 , where R 2 = n 1 2 + n 2 2 + n 3 2 . Each allowed energy state corresponds to node in N space ( n 1 , n 2 , n 3 ) . The number of particles corresponds to the number of states (nodes) in the first octant, within a sphere of radius, R . This number is given by: N = 2 ( 1 8 ) ( 4 3 ) π R 3 , where the factor 2 accounts for two states of spin. The density of states is found by differentiating this expression by energy:
g ( E ) = π V 2 ( 8 m e h 2 ) 3 / 2 E 1 / 2 . Integrating gives: E = 3 5 E F .

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Questions & Answers

plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
BARISUA Reply
Are beta particle and eletron are same?
Amalesh Reply
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
what is meant by Z in nuclear physic
Shubhu Reply
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
what is CHEMISTRY
trpathy Reply
it's a subject
Akhter
it's a branch in science which deals with the properties,uses and composition of matter
Eniabire
what is a Higgs Boson please?
FRANKLINE Reply
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of
BATTULA Reply
what is the black body of an ideal radiator
Areej Reply
uncertainty principles is applicable to
Areej
fermions
FRANKLINE
what is the cause of the expanding universe?
FRANKLINE
microscopic particles or gases
Areej
Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart. One explanation for dark energy is that it is a property of space.
Areej
Thanks for your contribution Areej.
FRANKLINE
no problem
Areej
what is photoelectric equation
HIMANSHU Reply
How does fringe intensity depend upon slit width in single slit diffraction?
Abhishek Reply
intensity seems to be directly proportional radius of slit
Mathieu
what are the applications of Bernoulli's equation
Shaukat
VOLTE
Md Reply
what is Draic equation
M.D
about nuclear angular momentum
rahul Reply
what is spin
MUKESH Reply
Practice Key Terms 6

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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