Question

rules for \filling\ energy levels:

1. pauli exclusion principle: one atomic orbital can accommodate no more than two electrons, and these electrons must have opposing spins.
2. hunds rule: within a group of orbitals of identical energy (i.e all the 2p orbitals), electrons enter empty orbitals whenever possible before being paired up.
3. aufbau principle: how the electrons fill the orbitals. \build up of energy levels.\ 1s. 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc.

c. identify the rule that is violated by each orbital diagram.
d. write the electron configuration of the following ions.

1. o²-
2. k+
3. na¹+

e. write the electron configuration of the following using the noble gases.

1. al
2. au
3. hg

Explanation:

Step1: Analyze orbital diagram a

According to the Aufbau principle, electrons should fill the lower - energy 4s orbital before the 3d orbital. In diagram a, the 4s orbital is filled but the 3d orbital is empty. This violates the Aufbau principle.

Step2: Analyze orbital diagram b

In the 4s orbital of diagram b, there is only one electron while according to the Pauli Exclusion Principle, if an orbital has an electron, it can have a maximum of two electrons with opposite spins. Here, the 4s orbital is not filled properly (it should have two electrons if it starts to be occupied in the context of electron - filling rules), violating the Pauli Exclusion Principle.

Step3: Analyze orbital diagram c

The 4s orbital in diagram c has two electrons (paired) which is correct. But according to the Aufbau principle, the 4s orbital should be filled before the 3d orbital. Since the 3d orbital is filled first (assuming the overall electron - filling order), this violates the Aufbau principle.

Step4: Analyze orbital diagram d

In the 3d orbitals of diagram d, electrons are singly occupied but they all have the same spin. According to Hund's Rule, electrons in degenerate (same - energy) orbitals should have parallel spins when entering empty orbitals. But here, there is no violation of Hund's Rule. However, the 4p orbital is empty while the 3d orbital is filled. According to the Aufbau principle (electrons fill orbitals in order of increasing energy: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p), the 4s should be filled before 3d and 4p should be filled after 3d. Since 4s is not filled (assuming the electron - filling process), this violates the Aufbau principle.

Step5: Analyze orbital diagram e

In the 4p orbital of diagram e, the first orbital has two electrons (paired) while the other two 4p orbitals are empty. According to Hund's Rule, electrons should enter empty orbitals of the same energy (degenerate orbitals) one at a time with parallel spins before pairing up. So, this violates Hund's Rule.

Step6: Write electron configuration of \(O^{2 -}\)

Oxygen has an atomic number \(Z = 8\). \(O^{2-}\) has \(8 + 2=10\) electrons. The electron configuration is \(1s^{2}2s^{2}2p^{6}\)

Step7: Write electron configuration of \(K^{+}\)

Potassium has an atomic number \(Z = 19\). \(K^{+}\) has \(19- 1 = 18\) electrons. The electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}\)

Step8: Write electron configuration of \(Na^{1+}\)

Sodium has an atomic number \(Z = 11\). \(Na^{+}\) has \(11 - 1=10\) electrons. The electron configuration is \(1s^{2}2s^{2}2p^{6}\)

Step9: Write electron configuration of \(Al\) using noble - gas notation

Aluminum has an atomic number \(Z = 13\). The noble - gas core is \([Ne]\) (Neon has 10 electrons). The remaining \(13 - 10=3\) electrons. The electron configuration is \([Ne]3s^{2}3p^{1}\)

Step10: Write electron configuration of \(Au\) using noble - gas notation

Gold has an atomic number \(Z = 79\). The noble - gas core is \([Xe]\) (Xenon has 54 electrons). The remaining \(79 - 54 = 25\) electrons. The electron configuration is \([Xe]4f^{14}5d^{10}6s^{1}\) (due to electron - pairing and stability considerations, there is a deviation from the simple Aufbau - based configuration)

Step11: Write electron configuration of \(Hg\) using noble - gas notation

Mercury has an atomic number \(Z = 80\). The noble - gas core is \([Xe]\) (54 electrons). The remaining \(80 - 54=26\) electrons. The electron configuration is \([Xe]4f^{14}5d^{10}6s^{2}\)

Answer:

C.
a. Aufbau principle
b. Pauli Exclusion Principle
c. Aufbau principle
d. Aufbau principle
e. Hund's Rule

D.

1. \(1s^{2}2s^{2}2p^{6}\)
2. \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}\)
3. \(1s^{2}2s^{2}2p^{6}\)

E.

1. \([Ne]3s^{2}3p^{1}\)
2. \([Xe]4f^{14}5d^{10}6s^{1}\)
3. \([Xe]4f^{14}5d^{10}6s^{2}\)