# 9.8 Superconductivity  (Page 5/12)

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Determine the lowest three rotational energy levels of ${\text{H}}_{2}.$

${E}_{0r}=7.43\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{eV}$ ; $l=0;{E}_{r}=0\phantom{\rule{0.2em}{0ex}}\text{eV}$ (no rotation);
$l=1;{E}_{r}=1.49\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\phantom{\rule{0.2em}{0ex}}\text{eV}$ ; $l=2;{E}_{r}=4.46\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\phantom{\rule{0.2em}{0ex}}\text{eV}$

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

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.

Why is bonding in ${\text{H}}_{2}{}^{+}$ favorable? Express your answer in terms of the symmetry of the electron wave function.

Astronomers claim to find evidence of ${\text{He}}_{2}$ 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.

Show that the moment of inertia of a diatomic molecule is $I=\mu {r}_{0}^{2}$ , where $\mu$ is the reduced mass, and ${r}_{0}$ is the distance between the masses.

Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by $\stackrel{\text{−}}{E}=\frac{1}{2}{E}_{\text{F}}.$

$\sum _{1}^{N\text{/}2}{n}^{2}=\frac{1}{3}{\left(\frac{N}{2}\right)}^{3},$ so $\stackrel{\text{−}}{E}=\frac{1}{3}{E}_{F}$

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 ${B}_{\text{c}}\left(0\right).$ Assume ${T}_{\text{c}}=9.3\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$

T (in K) ${B}_{\text{c}}\left(T\right)$
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

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.

Transition in the rotation spectrum are observed at ordinary room temperature ( $T=300\phantom{\rule{0.2em}{0ex}}\text{K}$ ). 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.

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

a. ${E}_{F}=7.11\phantom{\rule{0.2em}{0ex}}\text{eV}$ ; b. ${E}_{F}=3.24\phantom{\rule{0.2em}{0ex}}\text{eV}$ ; c. ${E}_{F}=9.46\phantom{\rule{0.2em}{0ex}}\text{eV}$

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

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

$9.15\approx 9$

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

## Challenge problems

For an electron in a three-dimensional metal, show that the average energy is given by $\stackrel{\text{−}}{E}=\frac{1}{N}\underset{0}{\overset{{E}_{\text{F}}}{\int }}Eg\left(E\right)dE=\frac{3}{5}{E}_{\text{F}},$

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 $\left({n}_{1},{n}_{2},{n}_{3}\right)$ . 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: $N=2\left(\frac{1}{8}\right)\left(\frac{4}{3}\right)\pi {R}^{3},$ where the factor 2 accounts for two states of spin. The density of states is found by differentiating this expression by energy:
$g\left(E\right)=\frac{\pi V}{2}{\left(\frac{8{m}_{e}}{{h}^{2}}\right)}^{3\text{/}2}\phantom{\rule{0.2em}{0ex}}{E}^{1\text{/}2}$ . Integrating gives: $\stackrel{\text{−}}{E}=\frac{3}{5}\phantom{\rule{0.2em}{0ex}}{E}_{\text{F}}.$

is this a physics forum
explain l-s coupling
how can we say dirac equation is also called a relativistic equation in one word
what is the electronic configration of Al
what's the signeficance of dirac equetion.?
what is the effect of heat on refractive index
As refractive index depend on other factors also but if we supply heat on any system or media its refractive index decrease. i.e. it is inversely proportional to the heat.
ganesh
you are correct
Priyojit
law of multiple
Wahid
if we heated the ice then the refractive index be change from natural water
Nepal
can someone explain normalization condition
Swati
yes
Chemist
1 millimeter is How many metres
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material.
What is photoelectric effect
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
why does not electron exits in nucleaus
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
expression for photon as wave
Are beta particle and eletron are same?
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
beta particle is of two kind beta plus and beta minus ,beta minus is electron and beta plus is positron
Nepal
beta particles are none but positive charged electron
Priyojit
which is ejected from nucleus
Priyojit
when nutron converts to proton it splits to two part one proton and the minus part ejected as beta
Priyojit
both are same things only the difference is that beta partical ejected from the neuclus and electrons revolves round the neuclus.
Sibghat