Problems: (2.1)Calculate the diamagnetic orbital susceptibility of a gas of hydrogen atoms (with number density 1020 m)in the ground state,and compare this with the entirely of water).What magnetic field would be necessary to induce the same magnetic moment in the duck as is contained in a magnetized iron filing?Repeat the calculation for a cow. (2.3)Calculate the mass 249.7 g)in a field of 1 T at 10 K. (2.4)Using the expressions for the partition function and the Helmholtz function of a spin-1/2 particle in a magnetic field B from eans 2.29 and 2.30 respectively, show that for such non-interacting particles per unit volume, the energy E pe unit volume is given by 公=-e8an(给）】 the heat capacity per unit volume is given by c(需}a(》) and the entropy per unit volume is given by s[(c(器)》-器m(e】 (2.5)Show that Hund's rules for a shell of angular momentum 1 and containing n electrons can be summarized by S=21+1-2☑+1-m L=S12l+1-m川 J=S121-nl. (2.6)Find the term symbols for the ground states of the ions (a)Ho3+(4f10), (b)Er3+(4f11),(c)Tm3+(4f12),and(d)Lu3+(4f14). Chapter Three:Environments 1.Teaching aims Understand the physical picture of the interactions between an atom and its immediate surroundings: Determine the magnetic ground of 3d ions under an octahedral or tetrahedral crystal field. Problems： (2.1) Calculate the diamagnetic orbital susceptibility of a gas of hydrogen atoms (with number density 1020 m-3) in the ground state, and compare this with the paramagnetic spin susceptibility at 100 K. (2.2) Estimate the diamagnetic susceptibility of a duck (assume it is composed entirely of water). What magnetic field would be necessary to induce the same magnetic moment in the duck as is contained in a magnetized iron filing? Repeat the calculation for a cow. (2.3) Calculate the paramagnetic moment of a crystal (with dimensions 2 mm x 2 mm x 2 mm) of CuSO4 5H2O (see Table 2.1, density 2286 kg m- 3 , relative molecular mass 249.7 g) in a field of 1 T at 10 K. (2.4) Using the expressions for the partition function and the Helmholtz function of a spin-1/2 particle in a magnetic field B from eqns 2.29 and 2.30 respectively, show that for n such non-interacting particles per unit volume, the energy E per unit volume is given by the heat capacity per unit volume is given by and the entropy per unit volume is given by (2.5) Show that Hund's rules for a shell of angular momentum l and containing n electrons can be summarized by (2.6) Find the term symbols for the ground states of the ions (a) Ho3+ (4f10), (b) Er3+ (4f11), (c) Tm3+ (4f 12), and (d) Lu3+ (4f14). Chapter Three: Environments 1. Teaching aims Understand the physical picture of the interactions between an atom and its immediate surroundings; Determine the magnetic ground of 3d ions under an octahedral or tetrahedral crystal field