مسائل في فيزياء الحالة الصلبة

المشرف الاستاذ: عبدالرحمن, الاخوان الكرام الاعضاء

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Superconductivity:

1. Estimate the drop in temperature of a superconducting specimen, initially at T = T

C ( <<1) in which the superconducting state is destroyed by the application of field B > Bc(T).
2. The critical field, Bc(T) for a superconductor follows the expression

20

()1cCBTBTT

Show this expression leads to

230230

232nscccnscccSSBTTTTTandCCBTTTTT  (cgs unit is used)
for entropy and heat capacity differences, per unit volume; n refers to the normal state and s to the superconducting state.

Diamagnetism:
3.

The wave function of the hydrogen atom in its ground state (1s) is

0

/301raea 

where . The charge density is

22100/0.52810ame2(,,)xyze.
(a) Show that for this state

22 0

3ra

(b) Calculate the molar diamagnetic susceptibility of atomic hydrogen.

Paramagnetism:
4.

Consider the case of an atom with two interacting spin-1/2 electrons. The ground state of such an atom can be a singlet with S= 0 or a triplet with S= 1. Let the energy difference between the single and triplet state is . If  > 0, the ground state is singlet and  < 0, the ground state is triplet.

(a)
Find the expression for the susceptibility ().

(b) Sketch () versus

/kT for the case  > 0 and  < 0 where k is the Boltzmann constant.
5. Some bacteria can be found living in quite unattractive places such as oil and sewage disposal plants. A bacterium that lives in an absolutely dark and essentially homogeneous soup faces a serious navigational problem if he must sometimes rise for oxygen and then descend for an important part of his dinner.
One class of bacteria has solved the problem by incorporating an iron oxide magnet inside its cell. Discuss the following questions quantitatively making clear the nature of the necessary rough approximations used.

(a)
Why not sense the pressure gradient in the fluid instead of using a magnet ?
(b)
Estimate the minimum magnetic moment that could be used to line up bacterium
(c)
Assuming 10-4 cm for the length of the magnetic needle, estimate the minimum diameter
(d)
Why is a needle better than a spherical magnet ?

6. The valence electron concentration per unit volume of Sodium is 2.65 x10

28 m-3 and its Fermi energy is 3.22 eV. Determine the paramagnetic susceptibility of Sodium and find its diamagnetic contribution if the measured susceptibility is p = 7.2 x10-6 (in SI unit).

Ferromagnetism:

7. (

a) For a ferromagnet with J = ½ and g = 2 , show that the specific heat that arises from the spontaneous magnetization is given by

222

(1)(/)[(/{1})ccCmmNTTTTm for T < TC

where

m = M(T)/M(0), N is the Avagadro’s number and k is the Boltzmann constant.

(b) Show that near the Curie temperature (TC), 3322CTCNT

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