# 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 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
what is meant by Z in nuclear physic
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
miss sanjana your question is wrong...question should be no of nucleus present in an atom...and answer is 1...
Owais
Owaise is right
Gitanjali
Z = number of protons in a nucleus of an atom
Shashikanth
Note on spherical mirrors