Problem+Set+8


 * Problem Set 8**


 * 1. In the quantum mechanical model of the atom elections are said to occupy //orbitals//. Explain how this could be misleading. Describe another analogy to the solutions of Schrödinger’s equation.**

Orbitals imply that the election orbits in around the nucleus of an atom in a certain path and where it will be at all times. But we know that Schrodinger’s equation solves for the area/region where an electron is predicted to be found 95% of the time; they aren’t orbiting around the nucleus like the moon around Earth. In quantum meachnics, it is impossible to predict exactly where an electron will be. A good analogy of an orbital would be a map that shows where an electron will most likely be, because we can only predict where we think it will be, we can’t be certain of where the electron is all the time. (Sam Crowe) Well stated. Yes, the idea is that an "orbital" describes a three dimensional volume in space where an electron could be found in that energy level/sublevel. It's best to think of them as clouds. (M. Grdinic)


 * 2. Explain how the quantum mechanical orbitals relate to Heisenberg's Uncertainty Principle.**

Orbitals show an area of probability in which an electron can be found, and since it is not an exact position of the electron, it is a perfect example of the Uncertainty Principle because it is basically impossible to know the exact location of the electron at a quantum scale. We can only guess and make predictions for the probable locations of the electron. It is all based on probability, and the orbitals just mark the area of the highest probable region. (Shoshi Center) Great!. (M. Grdinic)


 * 3. Write out the electron configuration of carbon and using the //Play-Doh//, build a model showing all of the orbitals that are occupied by the electrons.**

Carbon: 1s^2 2s^2 2p^1 Hmmm, I would check with Marielle's comment below. (M. Grdinic) As for the play-doh, no access to it, but 1s would have 2 electrons in it, 2s would also have 2 electrons in it, and one direction of 2p would have 1 electron in it. (Jeremy Chin) Doesn't carbon have 6 electrons? would there be 2p^2? (marielle billig)


 * 4. Which of the following electron transitions would result in the emission of energy?**

(Daniel Newman) 2d doesn't exist so d. would be **no**, and e. would have to be B because it has the greatest change in energy (Shoshi Center) Good catch Shoshi. (M. Grdinic)
 * a. 3p to 3s**--yes. The electron goes from a higher energy level to a lower energy level emitting a little amount of energy.
 * b. 3p to 4p**--no. The electron goes to a higher energy level so it does not emit energy.
 * c. 2s to 2p**--no. The electron goes to a higher energy level so it does not emit energy.
 * d. 4f to 2d**--yes. The electron goes from a higher energy level to a lower energy level emitting a very large amount of energy. The better answer is that no emission would occur because the rules of quantum mechanics forbid the existence of a 2d orbital. (M. Grdinic)
 * e. Which of the transitions would involve the most amount of energy?** The quantum jump from 4f to 2d emits the largest quantity of energy.


 * 5. Using the four quantam numbers explain why we do not have the following orbitials: ok well someone was supposed to do this...**

If n=1 then l cannot equal 1 because no such orbitals can exist. (jeremy chin) The orbitals can't overlap. 2d would become 2p or 3s. The quantum number "n" cannot equal "l."
 * a. 1p**
 * b. 2d**

The orbitals can't overlap. 2d would become 2p or 3s. The quantum number "n" cannot equal "l."

The orbitals can't overlap. 2d would become 2p or 3s. The quantum number "n" cannot equal "l." there are too many orbitals below 4f, so including a 3f would be conflicting with the other, lower energy orbitals. (The Jeremies) (Andrew Blank) <--- Boy Ach!!
 * c. 3f**

It's not necessarily the overlapping issue. Remember, even though our drawings appear to have the orbitals overlapping, the mathematics show that they are distinct volumes with NO overlap. It doesn't make intuitive sense, but then again, nothing in quantum mechanics really does. But it does support the experimental observations. (M. Grdinic)


 * 14. Write out the electron configuration for the element carbon. Pick on of the highest energy electrons and write out the four quantum numbers associated with it.**

Carbon: 1s^2 2s^2 2p^ 2 (M. Grdinic) n=2 (as in //2//p) l=1 (sublevel p) ml=-1, 0, 1 Since you were asked to pick ONE of the electrons, you can't have all three values for ml. Remember each one represents one of the orientations (of the three possible). (M. Grdinic) ms= 1/2 (upspin) Or it could be down spin: -1/2. Don't forget the + symbol making it +1/2. (M. Grdinic) (Jeremy Chin)

(Jeremy Chin) (^electron configuration of Uranium- http://education.jlab.org/itselemental/ele092.html (marielle billig))
 * 6. Write out the full electron configuration for each of the following:**
 * a. N**: 1s^2 2s^2 2p^3
 * b. Mg**: 1s^2 2s^2 2p^6 3s^2
 * c. Na+**: 1s^2 2s^2 2p^6
 * d. U**: doesn't follow the same electron configuration because it's past the point where Aufbau applies.
 * ||  || 1s2 ||   ||   ||   ||   ||   ||   ||   ||
 * 2s2 ||  || 2p6 ||   ||   ||   ||   ||   ||
 * 3s2 ||  || 3p6 ||   || 3d10 ||   ||   ||   ||
 * 4s2 ||  || 4p6 ||   || 4d10 ||   || 4f14 ||   ||
 * 5s2 ||  || 5p6 ||   || 5d10 ||   || 5f3 ||   ||
 * 6s2 ||  || 6p6 ||   || 6d1 ||   ||   ||   ||
 * 7s2 ||  ||   ||   ||   ||   ||   ||


 * 7. A few elements have electron configurations that don't follow the rules. Give an example of one of these elements and explain why this is the case.**

There are many exceptions to the Aufbau Principle after Vanadium (atomic number 23), and Chromium is an example. Chromium is an exception to the rule because half-filled sublevels are not as stable as filled sublevels, but they are more stable than some other configurations. If Chromium is given half-filled sublevels 3d and 4s (1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1), it is more stable than completely filling the 4s sublevel and only filling part of the 3d sublevel. (Alex Kaplan)