# Quantum Numbers & Electron Configurations

Would highly appreciate detailed work shown/ explanation on how you got your answer. This entire chapter makes little sense to me. (P.S. If answers are hand written, please do not write in cursive for I have a difficult time reading it)

1. What is the maximum number of electrons that can occupy each of the following subshells?

a) 4p

b) 5f

c) 2s

d) 3d

2. Write the condensed electron configurations for the following atoms:

a) Sulfer

b) Iron

c) Silver

d) Antimony

e) Chromium

f) Platinum

3. Determine if the following sets of quantum numbers are permissible for an electron in a hydrogen atom. (If it is permissible give the orbital type, if it is not permissible, explain why):

a) n=3, l=3, m=1

b) n=2, l=1, m=0

c) n=5, l=2, m=-3

d) n=4, l=3, m=2

4. What is the maximum number of electrons in an atom that can have the following quantum numbers?

a) n=3, l=2

b) n=1, s= 1/2

c) n=2, m=0

d) n=4, l=3

5. Determine what is wrong with the following electron configurations for atoms in their ground states and correct it:

a) 1s^2 2s^2 2p^6 3s^2 2d^1

b) [Ar] 4s^2 4d^10 4p^2

c) [Kr] 3d^2 4s^2

6. List the possible values for l and m when:

a) n=2

b) n=4

c) n=1

d) n=6

7. Draw the orbital diagrams for the valence electrons of each of the following elements and indicate how many unpaired electrons each has:

a) Aluminum

b) Vanadium

c) Rubidium

d) Molybdenum

e) Arsenic

f) Chlorine

g) Copper

I know this is a lot of questions to be asking, I just went through the chapter and pulled out review questions from almost every section I did not understand.

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#### Solution Preview

Firstly, this is a useful resource to read up on for review:

http://chemistry.about.com/od/electronicstructure/a/quantumnumber.htm

1) Electron subshells.

An electron subshell are volumes of space where electrons can orbit around a nucleus. As you can imagine, the more electrons there are, the more crowded it gets. Remember that electrons don't like to be close to each other, but are attracted to the nucleus. As a result, they tend to fall into orbits which are stable enough for them to keep occupying. These orbits are mathematically predictable, and the subshells represent these orbits. Since it's impossible to determine the exact trajectory by which an electron, under the influence of the nucleus and other electrons at a single point in time, will follow, the subshells are actually volumes of space where the electron has a probability of occupying.

The numbers behind the names of the subshells denote the energy level. If you recall from very basic chemistry, such as the Bohr model of the atom, electrons occupied energy levels. For example, hydrogen has one electron, occupying energy level 1. Carbon has 6 electrons, 2 of which are in level 1 and 4 of which are in level 2.

The letters (s, p, d etc.) are the possible orbitals within that energy level. The closer an electron is to the nucleus, the less room it has to manuever, but the farther it goes away from the nucleus, the more possibility there is for alternate orbits, and thus, alternate trajectories within an energy level. This is why energy level 1 only has a s-orbital, but energy level 3 has 3s, 3p, 3d. Each increasing orbital can carry more and more electrons, but each orbital for each energy level can only hold so much, albeit in increasing amount.

There's a general rule: s-orbitals always hold 2, p-orbitals 6, d-orbitals 10, f-orbitals 14.

As a result, the question is fairly simple, as the maximum number of electrons that can be held is entirely dependent on the orbital being described: 4p - 6 electrons. 5f - 14, 2s - 2, 3d - 10.

2) Continuing with the above core material, you can imagine it's quite difficult to describe large atoms using a description of all their energy levels and subshells. With something small like carbon, which has 6 electrons, the electron configuration is easy: 1s2 2s2 2p2. Notice, after the specific subshell name, the number of electrons occupying it are written. Also notice that although p-orbitals can hold a max of 6, in carbon's case there's only 2 electrons in 2p. Carbon only has 6 electrons total, and 2 are in each of the two s-orbitals in 1s and 2s.

Now imagine a bigger atom, say, Mg, with 12 electrons: 1s2 2s2 2p6 3s2. Already, it's getting long. So, a condensed configuration can be written ...

#### Solution Summary

The expert examines quantum numbers and electron configurations.

Atomic number and electronic configuration in a new universe

Suppose you take a trip to a distant universe and find that the periodic table there is derived from an arrangement of quantum numbers different from the one on Earth. The rules in that universe are:

1. principal quantum number n = 1, 2, ... (as on Earth);

2. angular momentum quantum number l = 0, 1, 2, ... n - 1 (as on Earth);

3. magnetic quantum number m_l = 0, 1, 2, ... l (only positive integers up to and including l are allowed);

4. spin quantum number m_s = - 1, 0, +1 (that is, three allowed values of spin).

a) Assuming that the Pauli exclusion principle remains valid in the alternate universe, what is the maximum number of electrons that can populate a given orbital there?

b) Write the electronic configuration of the elemental with atomic number 8 in the periodic table.

c) What is the atomic number of the second noble gas?

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