By Paul S. Epstein
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2(b) Express the typical ground-state electron configuration of an atom of an element in (a) Group 3, (b) Group 5, (c) Group 13 of the periodic table. 3(a) Identify the oxidation numbers of the elements in (a) MgCl2, (b) FeO, (c) Hg2Cl2. Identify the oxidation numbers of the elements in (a) CaH2, (b) CaC2, (c) LiN3. 4(a) Where in the periodic table are metals and nonmetals found? 4(b) Where in the periodic table are transition metals, lanthanoids, and actinoids found? (c) P4. 2(b) (c) N3−. Draw the Lewis (electron dot) structures of (a) SO2− 3 , (b) XeF4, Draw the Lewis (electron dot) structures of (a) O3, (b) ClF +3 , Summarize the principal concepts of the VSEPR theory of molecular shape.
The velocity and position are vectors, with both direction and magnitude. The magnitude of the velocity is the speed, v. 13) Like the velocity vector, the linear momentum vector points in the direction of travel of the particle (Fig. 8); its magnitude is denoted p. 14a) For motion confined to one dimension, we would write dpx /dt = Fx. 14a may be taken as the definition of force. 14b) where a is the acceleration of the particle, its rate of change of velocity. 14 will give the trajectory, the position and momentum of the particle at each instant.
The Taylor series for a function f(x) in the vicinity of x = a is ⎛ df ⎞ 1 ⎛ d2 f ⎞ f (x) = f (a) + ⎜ ⎟ (x − a) + ⎜⎜ 2 ⎟⎟ (x − a)2 2 ! ⎝ dx ⎠ a ⎝ dx ⎠ a +$ + = ∞ 1 ⎛ dn f ⎞ ⎜ ⎟ (x − a)n + $ n ! ⎜⎝ dx n ⎟⎠ a 1 ⎛ dn f ⎞ ∑ n! ⎜⎜⎝ dx n ⎟⎟⎠ (x − a)n n= 0 e x = 1 + x + 12 x 2 + $ = ∞ xn n=0 n ! 7c) n =1 Taylor series are used to simplify calculations, for when x << 1 it is possible, to a good approximation, to terminate the series after one or two terms. 8c) A series is said to converge if the sum approaches a finite, definite value as n approaches infinity.
