Related questions with answers

Find each root that is a real number. $-\sqrt[4]{256}$

Consider this geometric sequence: $3,6,12,24,48, \ldots$ a. What is the common ratio r? b. Call the general term of this sequence $A_{n}$ . Suppose that the starting subscript for the sequence is 0. Thus, the initial term is $A_{0}=3$ . What is a recursive formula for this sequence? What is a function formula for this sequence? Write both formulas in the form $"A_{n}=\ldots,$ ") c. Suppose the starting subscript is 1. Thus, $A_{1}=3$ . What is a recursive formula for the sequence in this case? What is a function formula? (Write both formulas in the form $"A_{n}=\ldots$ ." d. Compare the formulas in Parts b and c. Explain similarities and differences.

Find the mean and standard deviation of a normally distributed random variable X, given that P(X $\geqslant$ 80) = 0.1 and $\mathrm{P}(X \leqslant 30)=0.15$ .

Question

(a) Determine the radius of the smallest cation that can have (i) sixfold and (ii) eightfold coordination with the $\mathrm{Cl}^{-}$ ion (radius 181 pm). (b) Determine the radius of the smallest anion that can have (i) sixfold and (ii) eightfold coordination with the $\mathrm{Rb}^{+}$ ion (radius 149 pm).

Solution

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(a) The deviation of a structure from that expected on the basis of this rule is often taken to be an indication of a shift from ionic towards covalent bonding. A major source of unreliability, though, is the arbitrariness of ionic radii and their variation with coordination number.

The radius-ratio rule is derived by considering the geometrical problem of packing the maximum number of hard spheres of one radius around a hard sphere of a different radius.

Thus,

Radius-ratio, $\gamma = \dfrac{r_{\text{smaller}}}{r_{\text{larger}}}$