5answers - HOMEWORK #5 ANSWERS 1. Which of the following...

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HOMEWORK #5 ANSWERS 1. Which of the following sets of quantum numbers is allowed for an electron in a one electron atom? a. n=4, l =3, m=3, m s =0 b. n=3, l =1, m=2, m s = –1/2 c. n=2, l =0, m=1, m s =1/2 d. n=2, l =3, m=3, m s =1/2 e. n=6, l =5, m= –3, m s = –1/2 ANS: E Lets go through and figure out why a, b, c, and d are incorrect according to the rules we have for the possible values of the four quantum numbers. (a) we know that m s can only take on values of +1/2 and -1/2, so 0 is not an option. (b) we know that m can only take on values from – l to l , so m > l is not possible. (c) same reason as b. (d) we know that l can only take on values from 0 to n– 1 , so l > n is not possible. The only answer to fit all rules is (e). 2. Which of the following are possible quantum numbers for a 3d wave function in a hydrogen atom? a. n=2 l =3 m=3 b. n=3 l =0 m=0 c. n=3 l =3 m= –2 d. n=3 l =2 m= –1 e. none of the above ANS: D “n” is the principle quantum number (tells you the energy level), which in this problem is 3. l ” is the angular momentum quantum number (tells you the shape of the orbital) and takes on the integral values from 0 to (n-1) with zero being defined as “s”, and1=p, 2=d, 3=f. So in this case, l = 2 and the answer is d. 3. How many radial and angular nodes does a 4p orbital for a one electron atom have? a. 3 radial, 1 angular b. 2 radial, 2 angular c. 2 radial, 1 angular d. 2 radial, 0 angular e. 1 radial, 1 angular ANS: C The number of angular nodes is equal to l , and the number of radial nodes is equal to n – l 1 (page 182, point #2). Using this information, and that for a p orbital, l = 1, the number of angular nodes must be 1, and the number of radial nodes is 4 – 1 – 1 = 2.
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4. How many possible sets of quantum numbers (n, l , m, m s ) are there with n=4? a. 1 b. 4 c. 8 d. 16 e. 32 ANS: E There are 2 n 2 sets of quantum numbers for every value of n ; therefore, for n =4, there are 2x4 2 = 32 possible sets of quantum numbers (p. 184 of text). 5. The most probable distance for an electron in a 1s wavefuction in a hydrogen-like atom is at a distance equal to a o /Z. Given this information you would predict that Li 2 + would be a. 2 times larger than hydrogen b. 2 times smaller than hydrogen c. 3 times larger than hydrogen d. 3 times smaller than hydrogen e. no way to guess exactly due to shielding effects ANS: D If we are assuming that the most probable distance (a measure of the radius) is r = a o /Z, then the size will be inversely proportional to the atomic number, Z. Thus, since hydrogen is Z=1, and Li 2+ is Z=3 (both 1-electron species), we can conclude that the Li 2+ would be 3 times smaller than hydrogen. This is what we might expect since the larger positive charge in the nucleus of the lithium ion would attract the electron more than the single proton of the hydrogen nucleus. 6. The ground state 1s electron in which atom has an average distance closest to the nucleus?
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This note was uploaded on 04/30/2008 for the course CHEM 1411 taught by Professor Parkin during the Spring '08 term at Columbia.

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5answers - HOMEWORK #5 ANSWERS 1. Which of the following...

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