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
temperature T c = 3.4 K.
5.50 For lead superconductivity ensues at 7.19 K, when there is a zero applied magnetic 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 T m
2 , is the smallest unit
of flux).
5.3 Solutions
5.3.1 Crystal Structure
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
1
4
×
4
3
πr
3 or
π
3
r
3 . Volume of four spheres lying
within the cell is
4π
3
r
3 . Volume of the cell is a
3 or (2r )
3 . Therefore, the available
volume occupied by hard spheres in the simple cubic structure is
4πr
3 /3
(2r) 3 or
π
6
.
Fig. 5.1 Hard spheres in the
simple structure
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
temperature T c = 3.4 K.
5.50 For lead superconductivity ensues at 7.19 K, when there is a zero applied magnetic 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 T m
2 , is the smallest unit
of flux).
5.3 Solutions
5.3.1 Crystal Structure
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
1
4
×
4
3
πr
3 or
π
3
r
3 . Volume of four spheres lying
within the cell is
4π
3
r
3 . Volume of the cell is a
3 or (2r )
3 . Therefore, the available
volume occupied by hard spheres in the simple cubic structure is
4πr
3 /3
(2r) 3 or
π
6
.
Fig. 5.1 Hard spheres in the
simple structure