5.3 Solutions 299
5.47 Given that the maximum wavelength of photon to break up Cooper pair in tin
is 1. 08 × 10 −^3 m, calculate the energy gap.
5.48 A Josephson junction consists of two super conductors separated by a very
thin insulating layer. When a DC voltage is applied across the junction an
AC current is produced, a phenomenon called Josephson effect. Calculate the
frequency of the AC current produced when a DC voltage of 1. 5 μV is applied.
5.49 Use the BCS theory to calculate the energy gap for indium whose critical
temperatureTc= 3 .4K.
5.50 For lead superconductivity ensues at 7.19 K, when there is a zero applied mag-
netic field. When the magnetic field of 0.074 T is applied at temperature 2.0 K
superconductivity will stop. Find the magnetic field that should be applied so
that superconductivity will not occur at any temperature?
5.51 An ac current of frequency 1 GHz is observed through a Josephson junction.
Calculate the applied dc voltage.
5.52 If a superconducting Quantum Interference Device which consists of a 3 mm
ring can measure 1/5,000 of a fluxon, calculate the magnetic field that can be
detected (1 fluxon,φ 0 =h/2e= 2. 0678 × 10 −^15 Tm^2 , is the smallest unit
of flux).
5.3 Solutions..................................................
5.3.1 CrystalStructure...................................
5.1 The cross-section of the portions of four spheres each of radius r touching each
other and lying in a cell of edge a is shown in Fig. 5.1. The volume of each
sphere lying within the cell is^14 ×^43 πr^3 orπ 3 r^3. Volume of four spheres lying
within the cell is^43 πr^3. Volume of the cell isa^3 or (2r)^3. Therefore, the available
volume occupied by hard spheres in the simple cubic structure is^4 πr
(^3) / 3
(2r)^3 or
π
6.
Fig. 5.1Hard spheres in the
simple structure