PHY 445 / PHY 515

Advanced Physics Laboratory,

Answers to HW problems

  1. -The superconducting transition temperature of Al metal (1% accuracy)

    Tc=1.175 ± 0.002 K (CRC Handbook, 76th Edition; also Landolt Börnstein, III/21a p.7 for better than 10ppm pure Al monocrystal)

    Tc=1.181 K Landolt Börnstein, III/21a p.7 for 1ppm pure Al wire; there are a bunch of other numbers there as well for various samples. ) These two numbers are within the 1% accuracy.

  2. -YBa2Cu3O7 (5%)

    3. Tc= 92 ± 2 K (R.Cava et al., Phys. Rev. Letters, 58, 1676 (1987).) The critical temperature of this material varies with oxygen content, and it is difficult to get accurately reproducible values.

  3. -The lattice spacing of diamond at room temperature (100ppm)

    4. The size of the cubic unit cell is 3.5670 ± 0.0001 Angstrom at 25 oC. (CRC Handbook, 76th Edition; also Landolt Börnstein, III/6 p.4. An old edition of LB specifies a=3.55977 at 18 oC . )

  4. -The resistivity ratio of high purity platinum metal between the temperatures of 100oC and 0oC. (2%)

    5. Platinum is used as a thermometer material, and there are quite a few calibration tables around. The so called "American curve" from the "Temperature Handbook", Omega, (1989) p Z-88 yields RR=1.3916 ± 0.0005. This agrees well with the the resistivity curve published in Landolt-Bornstein, III/15a.

  5. -What is the magnetic field H (in Tesla) of a dipole moment of magnitude 1 Bohr magneton (exactly) at a distance of d=1.00nm in the direction of the dipole axis.

    H=m0 mB / (2p d3)=1.85 x 10 -3 T. The magnetic moment is 9.27 x 10-24J/T, the distance is d = 1 nm, and m0 = 4p x 10-7 Vs/Am2. The incorrect answers ranged over 16 orders of magnitude.

  6. -What is the Hall voltage, UH = RH I B / d , for a sample of doped germanium, where d = 0.1mm, B = 0.35T and I = 10-6A. The Hall coefficient RH is inversely proportional to the carrier density n = 9 x 1013cm-3 and to the electron charge.

    UH = RHIB/d, where the Hall coefficient is RH = 1/ne. The result is 0.243 mV. Two submissions were a factor of hundred large; one was a factor of ten high.

  7. -What is the frequency (in Hz) of electron spin resonance in magnetic field of 5 Gauss.

    From h n = 2mB B one gets n = 14 MHz.