Question

Mass number of mercury varies from 199.5 to X a.m.u and the corresponding
transition temperature Tc varies from 4.185 to 4.146 K respectively. Find X?​

Answer 1

V3Ge

V3Ga

V3Si

NbN

1.175

4.15

3.95

3.41

9.46

0.85

7.196

3.72

0.4

4.88

4.47

0.517

0.61

1.083

1.38

6.0

14.2

17.4

16.0

Nb 3 Sn

Nb3Al

Nb3Ge

Nb3Au

La3In

Ceramics

Bi2Sr2Ca2Cu3O10

Bi2Sr2CaCu2O9

Bi2Sr2CaCu2O8

(Ca1-XSrX)CuO2

(Ba,Sr)CuO2

(La,Sr)CuO2

YBa2Cu3O7

Tl2Ba2Ca2Cu3O10

TlBa2CaCu2O7

TlBa2Ca2Cu3O9

TlBa2Ca3Cu4O11

Hg4Tl3Ba30Ca30Cu45O47

(Tl4Ba)Ba4Ca2Cu10Oy

18.3

18.9

23.0

11.5

10.4

110

110

91-92

110

90

42

90

47

80

105

40

138*

240**

Table 4.1 Transition temperatures of some superconductors-(* discovered in 2006,

** discovered in 2009)

(ii) Persistent current

Consider a small amount of current is applied to a superconducting ring. The

superconducting current will keeps on flowing through the ring without any changes

in its value. This current is said to be persistent current. In a superconductor since

there is no resistive hear loss (i2R), the supercurrent will keeps on flowing until the

specimen is in the superconducting state.

(iii) Diamagnetic property

Consider a magnetic field is applied to a normal conducting material. The

magnetic lines of forces penetrate through the material. Consider a normal

conductor is cooled down to very low temperature for superconducting property. If it

is cooled down below the critical temperature, then the magnetic lines of forces are

ejected from the material. A diamagnetic material also repels the magnetic lines of

forces. So, the ejection of magnetic lines of forces, when the superconducting

material is cooled down is said to be the diamagnetic property. This property was

first observed by Meissner and hence this property is also called as Meissner effect.  

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(a) (b)

Fig.4.2 Diamagnetic property (a) Magnetic filed applied into a normal conductor

(b) magnetic filed applied into a superconductor

The diamagnetic property is easily explained using the following mathematical

treatment:

The magnetic flux density is given by,

B=μO(M+H)

For a superconducting material, B=0. Substituting, B=0, we get,

0=μO(M+H)

i.e., M=-H

 1

H

M



(4.1)

The negative value of the susceptibility shows the diamagnetic properties of the

superconducting material.

(iv) Application of magnetic field-Tuyn’s law

The superconducting materials exhibit the diamagnetic property only below

the critical field. If the magnetic field is increased, beyond a minimum value known

as critical field, the superconducting property of the material is destroyed, when the

field is equal to or greater than the critical magnetic field. The minimum magnetic

field required to destroy the superconducting property is known as the critical field.

The field required to destroy the superconducting property is given by













 2

2

() 1

C

C O T

H

T HT

(4.2)

where HC(T) is the critical field required to destroy the superconducting property at T

K, TC is the critical temperature, HO is the critical field required to destroy the  

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superconducting property at 0 K. Eq.(4.2) is known as Tuyn’s

(a) (b)

Fig.4.3 Magnetic field versus temperature (a) Application of magnetic field to a

superconductor, (b) magnetic filed versus temperature for Sn, Pb and Nb.

Explanation: