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Given that the radius of the Ca²⁺ and F^- ions are 1.03 Å and 1.36 Å, respectively, show that the packing fraction of the CaF₂(Fluorite) structure is 0.61.

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SOLID STATE physics
Consider a face centered cubic (fcc) crystal in which one atom is placed at each lattice point. The lattice constant is a = 0.7 \: nma=0.7nm. Calculate the volume density of atoms (i.e. number of atoms per unit volume) in units of cm^{-3}cm−3. Values within 5% error will be considered correct.
1.4 Plot the energy band-gap Eg versus the lattice constant for the two ternary compounds, In¡ „Ga,As and Al,InAs. Label the values for the binary compounds, InAs, GaAs, AIAS, and InP. The band-gap formulas at 300K are E,(In „Ga,As) = (0.36 + 0.505x + 0,555x² Eg(Al,In „As) = 0.36 + 2.35x + 0.24x?. Show on your plot the locations (and values) of the lattice match conditions for the InP substrate.
Diatomic astatine, At2, is the rarest, heaviest, and largest of the halogens. Astatine has an atomic weight of 210 Daltons, and At2 has a bond length of 300 pm. Use this information to determine its rotational constant, B, in units of cm-1 (you should keep only two significant figures). (Note: 1 Dalton = 1.66053 × 10-27 kg, 1 pm = 10–12 m.)
(4) Predict the structure of CsCl. Given: radius of Cs+= 0.160 nm, radius of Cl-=0.181nm. Calculate the radius ratio between Cs+ and Cl- and derive the coordination number (CN) based on the table below. Rcation/Ranion CN 0-0.155 2 3 0.155-0.225 0.225-0.414 0.414-0.732 0.732-1 1 4 6 8 12
The lowest frequency microwave transition of the 12CO molecule occurs at 3.8626 cm-'. This transition corresponds to the J= 0 → J= 1 rotational transition. (а) From the J= 0 →J=1 transition energy, calculate the rotational constant (in cm-') of the 12CO molecule. (b) What is the energy (in units of cm-l) for the J= 1→J=2 rotational transition of 12²CO? (c) Calculate the rotational constant for the 13CO molecule. (d) Using the 12CO or 13CO rotational constant, calculate the bond length for CO.
(a) State what the Fermi energy depends on according to the free-electron theory of metals and how the Fermi energy depends on that quantity. (b) Show that Equation 42.23 can be expressed as EF = (3.65 x 10-19)ne 2/3, where EF is in electron volts when ne is in electrons per cubic meter. (c) According to Table 42.1, by what factor does the free-electron concentration in copper exceed that in potassium? (d) Which of these metals has the larger Fermi energy? (e) By what factor is the Fermi energy larger? (f) Explain whether this behavior is predicted by Equation 42.23.
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(Z1e)(Z3e) (b) The attractive bonding force, F4, in an ionic bond is given by the formula F where z,, Z,valences of ions 1 and 2 respectively and r is the distance between the two ions. Determine the distance, r, between a Na and an Cl ion if the attractive force is 1.025 x 101º N, given that e 1.602 x 10–19C) and ɛ, = 8.85 x 1012 F/m.
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1.2 Below 24.5 K, Ne is a crystalline solid with an FCC structure. The interatomic interaction energy per atom can be written as: (1) 6 E(r) = -28 2E 14.45* (ii) (iii) – 12 13¹] (ev/atom) Where, & and o are constants that depend on the polarizability, the mean dipole moment, and the extent of overlap of core electrons. For crystalline Ne, & = 3.121 x 10-3 eV and a = 0.274 nm. 12.13 Show that the equilibrium separation between the atoms in an inert gas crystal is given by ro= (1.090) o. What is the equilibrium interatomic separation in the Ne crystal? Find the bonding energy per atom in solid Ne.

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