301 CH Worksheet 4 Key Dr. Sparks Major topics for this problem set: Quantum Mechanics Quantum Numbers Electron Configurations
Things you should know about the periodic table: Which columns are the: Alkali metals Alkaline earth metals Halogens Noble gases Transition metals Where are the metals? The nonmetals? Where is the dividing line between them? Where are the metalloids?
Things you should know: Definition of cation (positively charged ionic species) and anion (negatively charged).
1. What is the term for a region where there is zero probability of finding a particle? A region of zero probability is called a "node."
2. Consider the following wave as .
a. Sketch 2.
b. How many nodes exist? There are two nodes. They are marked as red dots on the figure above, where the values = 0.
3. Give a brief explanation of each of the following quantum numbers in your own words: n, l, ml, ms.
n = principal quantum number, the main energy levels, any positive integer starting at 1 l = azimuthal quantum number, shape of orbits, subshell, 0 to n-1. Numbers indicate s, p, d, f orbital shapes ml = magnetic quantum number, orientation of orbital, -l to l. Tells you the number of individual orbitals within one subshell. i.e. an s orbital l=0 has +0 and -0, or one orbital, while p (l=1) has three (-1, 0, +1) ms = spin quantum number, direction of spin, +1/2 or -1/2 (NOTE: The value for this number does not matter, just that there is a positive and negative value of equal magnitudes.)
4. True or False? The following set of quantum numbers is acceptable (0,0,0, +1/2). Explain.
False. The principal quantum number, n, corresponds to the volume of space in which an electron moves around a nucleus and can only be positive integers greater than 0. Therefore, 0 is not a principle quantum number.
5. How many electrons can have the following quantum numbers in an atom: n= 3, l=2?
10 electrons. For every subshell (l) there are -l to l possible orbitals (here, -2, -1, 0, 1, 2), each of which may contain two electrons with opposite spins.
6. State in your own words the Pauli exclusion principle. Which of the quantum numbers is it most concerned with?
In a given atom, all of the electrons must be described by a unique set of four quantum numbers (n, l, m and s). It is most concerned with ms, since for any value of n, l and m, s must be different, ensuring that the electrons have opposite spins. So, for our purposes, the Pauli exclusion principle states that any two electrons in the same orbital must have opposite spins.
7. True or False: An electron in a 3s orbital is always further from the nucleus than an electron in a 2s orbital. Explain your answer. False. Although orbitals help us to estimate the approximate distance an electron might be found from the nucleus, electrons are not strictly bound in a spherical orbit as predicted by Bohr. An electron occupying a 3s orbital can move closer or further away from the nucleus and consequently could be closer to the nucleus than an electron in the 2s orbital. Radial probability distributions are graphs that predict the most likely distance of an electron from the nucleus for a given orbital (See Figure 12.17 in Zumdahl). 8. In your own words, what does Hund's rule state?
Every orbital in a subshell must have one electron in it before any orbital can have a pair of electrons in it. In other words, we half fill all orbitals before completely filling any of them.
9. Now boil it all down: in the way simplest possible, define the Aufbau principle, the Pauli exclusion principle, and Hund's rule. (State them in just a few words that are usable to you in remembering them.)
Aufbau principle: electron orbitals are filled from lowest energy to highest energy. Pauli exclusion principle: only 2 electrons per orbital Hund's rule: electrons will distribute singly between orbitals of the same energy before they pair up. (Example: If there are 3 electrons and three orbits, there will be one electron in each orbit instead of one empty orbit, one orbit with one electron, and one orbit with 2 electrons.)
10.
In all of those above, be sure to count the arrows before and after to make sure you didn't miss any!
11. Write the electron configuration of gallium (Ga) in long notation and in short (noble gas) notation.
2 2 6 2 6 2 10 1
1s 2s 2p 3s 3p 4s 3d 4p
2 10 1
[Ar] 4s 3d 4p
2+
12. Write the electron configuration of a divalent vanadium cation (V ) in long and in short notation.
2 2 2 6 1 2 6 2 1
1s 2s 2p 3s 3p 4s 3d [Ar] 4s 3d
-
13. Write the electron configuration of a monovalent iodine anion (I ) in long and in short notation.
2 2 6 2 6 2 10 6 2 10 6
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p
2 10 6
[Kr] 5s 4d 5p
14. Which ground state element corresponds to the following electron configurations?
14 3 2
a. [Rn] 5f 6d 7s Dubnium (Db)
2 4
b. [Ne] 3s 3p Sulfur (S)
14 6 2
c. [Xe] 4f 5d 6s Osmium (Os)
14 10 1
d. [Xe] 4f 5d 6s Gold (Au), Gold would rather have a full d-orbital (5d10 6s1) than not (5d9 6s2) because it is less energy to fill the d-orbital.
15. In which region of the periodic table do we find most of the exceptions to Aufbau for neutral, ground state elements?
We find the most exceptions to the Aufbau principle for neutral, ground state elements in the transition metal region of the periodic table (both d-transition metals and f-transition metals). Chromium and copper are two examples of exceptions to the Aufbau principle.
16. Consider Pb3+. Predict the electron configuration of this cation.
The electron configuration of Pb is [Xe] 6s24f145d106p2 Hence, a first estimate at Pb3+ would be this minus three electrons: [Xe] 6s24f145d9 However, you see an almost filled d-orbital. This should send off "possible exception!" warning bells. Note that Pb3+ is isoelectronic with Au. We know a common exception with almost half- or almost fully-filled d-orbitals is to shift one from the s-orbital to the d-orbital. The electron configuration is: [Xe] 6s14f145d10
17. Write the electron configuration for silver. Try to give at least one example of an ion that would have an identical electron configuration.
1 10 3+
[Kr] 5s 4d Cd , In and Sn would all have the same electron configuration as Ag. Here again, you see the "filled d-orbital" exception.
+ 2+
18. Is the electron configuration for silver a violation of the Aufbau principle? Defend your assertion.
While silver's electron configuration *is* an exception to the normal order orbitals fill, it *is not* a
1 10
violation of the Aufbau principle. Silver's experimentally determined electron configuration is [Kr] 5s 4d . The Aufbau principle states that a ground state atom will have its electrons in their lowest energy possible,
1 10 2 9
so if [Kr] 5s 4d is what is observed, it is by definition lower in energy than [Kr] 5s 4d and thus Aufbau has not been violated.
3-
-
2+
19. What one adjective describes the following species: Ar, P , Cl , Ca ?
Isoelectronic.