(a) Data on a single crystal of $\mathrm{MnF}_{2}$ give $\chi_{m}=0.1463 \mathrm{cm}^{3} \mathrm{mol}^{-1}$ al 294.53 K. Identify the effective number of unpaired electrons in this compound and compare your result with the theoretical value. (b) Data on a single crystal of $\mathrm{NiSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}$ give $\chi_{\mathrm{m}}=6.00 \times 10^{-4} \mathrm{m}^{3} \mathrm{mol}^{-1}$ at 298 K. Identify the effective number of unpaired electrons in this compound and compare your result with the theoretical value.

In your own words, define and provide an example of a composite function.

Use your notes to identify events that show the Mongols'rise to power.

A two-sample data analysis is conducted to compare the efficiencies of workers who have and who have not taken a training course. A. If the confidence interval for the difference in the efficiencies of the two sets of workers extends from a negative value to a positive value so that it contains zero, then it should be concluded that it has been proved that the training method is effective. B. If the confidence interval for the difference in the efficiencies of the two sets of workers extends from a positive value to a positive value so that it does not contain zero, then it should be concluded that the training course has no effect on the efficiencies of the workers. C. Both of the above. D. Neither of the above.

What were the religious differences among East, West, and South Africa?

(a) Calculate the molar susceptibility of benzene given that its volume susceptibility is $-7.2 \times 10^{-7}$ and its mass density is $0.879\ \mathrm{g}\ \mathrm{cm}^{-1}$ at $25^{\circ} \mathrm{C}.$ b) Calculate the molar susceptibility of cyclohexane given that its volume susceptibility is $-7.9 \times 10^{-7}$ and its mass density is $811\ \mathrm{kg}\ \mathrm{m}^{-1}$ at $25^{\circ} \mathrm{C}.$

(a) The magnitude of the magnetic moment of $\mathrm{CrCl}_{3}$ is $3.81\ \mu_{\mathrm{B}}.$ How many unpaired electrons does the Cr possess? (b) The magnitude of the magnetic moment of $\mathrm{Mn}^{2+}$ in its complexes is typically $5.3\ \mu_{\mathrm{B}}.$ How many unpaired electrons does the ion possess?

Compare and contrast the polarization with the magnetization.

Describe the characteristics of the Fermi-Dirac distribution, contrast it with the Boltzmann distribution.

(a) A typical value for the Fermi energy is 1.00 eV. At 298 K, calculate the energy above the Fermi energy at which the probability has fallen to 0.25; express your answer in eV. (b) Repeat the calculation but this time for probability of 0.10 and Fermi energy of 2.00 eV.

(a) Poisson's ratio for polyethene is 0.45. What change in volume takes place when a cube of polyethene of volume $1.0\ \mathrm{cm}^{3}$ is subjected to a uniaxial stress that produces a strain of 1.0 per cent? (b) Poisson's ratio for lead is 0.41. What change in volume takes place when a cube of lead of volume $1.0\ \mathrm{dm}^{3}$ is subjected to a uniaxial stress that produces a strain of 2.0 per cent?

Poisson's ratio for polyethlene is 0.45 . What change in volume takes place when a cube of polyethylene of volume 1.0 cm$^3$ is subjected to a uniaxial stress that produces a strain of 1.0 per cent?

Poisson's ratio for lead is 0.41 . What change in volume takes place when a cube of lead of volume 1.0 dm$^3$ is subjected to a uniaxial stress that produces a strain of 2.0 per cent?

(a) The Young's modulus of polystyrene is 4.42 GPa. A polystyrene rod of diameter 2.0 mm is subject to a force of 500 N along its length. Calculate the stress and hence the percentage increase in the length of the rod when the stress is applied. (b) Calculate the force which needs to be applied to a polystyrene rod of diameter 1.0 mm to increase its length from 10.00 cm to 10.05 cm.

(a) The bulk modulus of polystyrene is 3.43 GPa. Calculate the hydrostatic pressure (stress) needed for a sample of this material to change volume by 1.0 per cent. (b) A sample of polystyrene of volume $1.0\ \mathrm{cm}^{2}$ is subjected to a hydrostatic pressure (stress) of 1000 bar. Calculate the volume of the sample after the pressure has been applied.