# 9.8 Superconductivity  (Page 5/12)

 Page 5 / 12

## Key equations

 Electrostatic energy for equilibrium separation distance between atoms ${U}_{\text{coul}}=-\frac{k{e}^{2}}{{r}_{0}}$ Energy change associated with ionic bonding ${U}_{\text{form}}={E}_{\text{transfer}}+{U}_{\text{coul}}+{U}_{\text{ex}}$ Critical magnetic field of a superconductor ${B}_{\text{c}}\left(T\right)={B}_{\text{c}}\left(0\right)\left[1-{\left(\frac{T}{{T}_{\text{c}}}\right)}^{2}\right]$ Rotational energy of a diatomic molecule ${E}_{r}=l\left(l+1\right)\frac{{\hslash }^{2}}{2I}$ Characteristic rotational energy of a molecule ${E}_{0r}=\frac{{\hslash }^{2}}{2I}$ Potential energy associated with the exclusion principle ${U}_{\text{ex}}=\frac{A}{{r}^{n}}$ Dissociation energy of a solid ${U}_{\text{diss}}=\alpha \frac{k{e}^{2}}{{r}_{0}}\left(1-\frac{1}{n}\right)$ Moment of inertia of a diatomic molecule with reduced mass $\mu$ $I=\mu {r}_{0}^{2}$ Electron energy in a metal $E=\frac{{\pi }^{2}{\hslash }^{2}}{2m{L}^{2}}\left({n}_{1}^{2}+{n}_{2}^{2}+{n}_{3}^{2}\right)$ Electron density of states of a metal $g\left(E\right)=\frac{\pi V}{2}{\left(\frac{8{m}_{e}}{{h}^{2}}\right)}^{3\text{/}2}\phantom{\rule{0.2em}{0ex}}{E}^{1\text{/}2}$ Fermi energy ${E}_{\text{F}}=\frac{{h}^{2}}{8{m}_{e}}{\left(\frac{3N}{\pi V}\right)}^{2\text{/}3}$ Fermi temperature ${T}_{\text{F}}=\frac{{E}_{\text{F}}}{{k}_{\text{B}}}$ Hall effect ${V}_{\text{H}}=uBw$ Current versus bias voltage across p-n junction ${I}_{\text{net}}={I}_{0}\left({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1\right)$ Current gain ${I}_{c}=\beta {I}_{B}$ Selection rule for rotational energy transitions $\text{Δ}l=±1$ Selection rule for vibrational energy transitions $\text{Δ}n=±1$

## Conceptual questions

Describe two main features of a superconductor.

How does BCS theory explain superconductivity?

BSC theory explains superconductivity in terms of the interactions between electron pairs (Cooper pairs). One electron in a pair interacts with the lattice, which interacts with the second electron. The combine electron-lattice-electron interaction binds the electron pair together in a way that overcomes their mutual repulsion.

What is the Meissner effect?

What impact does an increasing magnetic field have on the critical temperature of a semiconductor?

As the magnitude of the magnetic field is increased, the critical temperature decreases.

## Problems

At what temperature, in terms of ${T}_{C}$ , is the critical field of a superconductor one-half its value at $T=0\phantom{\rule{0.2em}{0ex}}\text{K}$ ?

$T=0.707\phantom{\rule{0.2em}{0ex}}{T}_{\text{c}}$

What is the critical magnetic field for lead at $T=2.8\phantom{\rule{0.2em}{0ex}}\text{K}$ ?

A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a $50\text{-}\text{Ω}$ resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?

61 kV

A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius 1.5 mm. What maximum current can the solenoid carry if the wire is to remain superconducting?

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are ${r}_{0}=0.255\phantom{\rule{0.2em}{0ex}}\text{nm}$ apart. Determine the electrostatic potential energy of the atoms. The electron affinity of F is 3.40 eV and the ionization energy of K is 4.34 eV. Determine dissociation energy. (Neglect the energy of repulsion.)

$\begin{array}{ccc}\hfill {U}_{\text{coul}}& =\hfill & -5.65\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \\ \hfill {E}_{\text{form}}& =\hfill & -4.71\phantom{\rule{0.2em}{0ex}}\text{eV},\phantom{\rule{0.2em}{0ex}}{E}_{\text{diss}}=4.71\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \end{array}$

For the preceding problem, sketch the potential energy versus separation graph for the bonding of ${\text{K}}^{+}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{\text{Fl}}^{\text{−}}$ ions. (a) Label the graph with the energy required to transfer an electron from K to Fl. (b) Label the graph with the dissociation energy.

The separation between hydrogen atoms in a ${\text{H}}_{2}$ molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV.

${E}_{0r}=7.43\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{eV}$

The characteristic energy of the ${\text{Cl}}_{2}$ molecule is $2.95\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}\text{eV}$ . Determine the separation distance between the nitrogen atoms.

How does, ray of light coming form focus, behaves in concave mirror after refraction?
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
DHEERAJ
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
why we have physics
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
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.?