Chem

Describe the Pauli exclusion principle and give an example

:The Pauli exclusion principle states that no two electrons can have the same set of four quantum numbers.For example, consider the two electrons in a helium atom. Both electrons occupy the same 1s orbital, and they must be spin-paired (one electron is spin up while the other is spin down), as required by the Pauli exclusion principle. Thus, both electrons have n = 1, l= 0, ml = 0, and one electron has ms = +½ while the other has -½.

Write a set of quantum numbers that could describe a 3d orbital.

A 3d orbital must have n = 3 and l = 2. Furthermore, when l = 2, there are five allowed values of ml = -2, -1, 0, +1, +2, and ms can be either -½ or +½. Thus, the allowed values for the 3d subshell are: n = 3; l = 2; ml = -2, -1, 0, +1, +2; ms = -½ or +½.

Write a set of quantum numbers that could describe a 4f orbital.

A 4f orbital must have n = 4 and l = 3. Furthermore, when l = 3, there are seven allowed values of ml = -3, -2, -1, 0, +1, +2, +3, and ms can be either -½ or +½. Thus, the allowed values for the 4f subshell are: n = 4; l = ; ml = -3, -2, -1, 0, +1, +2, +3; ms = -½ or +½.

What is meant by the term boundary surface?

A boundary surface contains a defined region of space in which there is a 90 % probability of finding an electron.

How many electrons can a 5d subshell hold?

A d subshell must have l = 2, and it therefore has five allowed values of ml: -2, -1, 0, +1, and +2. Since each of the five orbitals can hold two electrons, the 5d subshell can hold a maximum of 10 electrons.

Sketch ψ2 for a 1s orbital in a hydrogen atom. Sketch the radial probability distribution function for a 1s orbital in a hydrogen atom. How are the two sketches different? What is significant about these differences?

A plot of ψ2 vs r for a 1s orbital indicates the greatest probability of finding an electron is at the nucleus; however, this cannot be true because electrons are found outside the nucleus. Therefore, scientists correct for this limitation using the concept of radial probability, which represents the total probability of finding and electron within a spherical shell at r from the nucleus. The radial probability distribution function is the product of the probability density and the volume of the thin shell at a distance r from the nucleus.

Describe the significance of a wave function

A wave function (ψ) represents the characteristics of the standing wave of an electron confined to a specific energy level in an atom. Practically speaking, however, the wave function of an electron has no real physical significance.

What is electron spin?

An electron's spin, like its charge, is an intrinsic characteristic. Spin is quantized and there are two allowed orientations: spin up and spin down. An electron's spin is described by the electron spin quantum number, ms, which has two allowed values, +1/2 for electrons that are spin up and -1/2 for electrons that are spin down. Because of their spin, electrons generate a tiny magnetic field around them.

Explain how the distance from the nucleus affects orbital energy. Why are orbitals with a larger value of n higher in energy?

Coulomb's law states that as the separation between oppositely charged particles decreases, the energy becomes increasingly more negative. Electrons in smaller orbitals are closer to the nucleus than electrons in larger orbitals. As a result, smaller orbitals are lower-energy orbitals than larger orbitals. As n increases and orbitals become larger, the energy of the orbitals becomes less negative, or higher, in energy.

What is meant by effective nuclear charge?

Effective nuclear charge is the nuclear charge experience by the outer electrons. Effective nuclear charge is always some value less than the nuclear charge because of the shielding of outer electrons by core electrons.

What is meant by the term electron density?

Electron density (ψ2) refers to the probability of finding an electron in a volume of space around a central point.

How many electrons can a 6f subshell hold

For the given subshell, determine the number of allowed values of ml, which represents the number of orbitals. Each orbital can hold a maximum of two electrons.

Describe Hund's rule and give an example.

Hund's rule states that, when electrons fill degenerate orbitals within the same subshell, one electron is placed in each orbital before the electrons are paired up. This ultimately decreases electron-electron repulsions.For example, the electron configuration of carbon has 6 total electrons. The first two electrons are placed in the 1s orbital, then two more electrons are placed in the 2s orbital, leaving two remaining electrons. These final two electrons are placed in separate 2porbitals, as required by Hund's rule. See Figure 8.2.13 for an illustration.

.Explain why the energy scale used to rank orbitals from highest energy to lowest energy is negative? What is the energy of a free electron?

In Coulomb's law, which describes the energy of attraction between oppositely charged particles, q+ is the positive charge of the nucleus, q- is the negative charge of the electron in its orbital, and r is the distance between them. Since q+ is a positive number and 3s4s q- is a negative number, the value of E must be negative. The energy of attraction of a free electron - an electron infinitely separated from the nucleus - is zero.

Explain the difference between a shell and a subshell of orbitals.

Orbitals that have the same value of n belong to the same shell of orbitals, whereas orbitals that have the same values of both n and l belong to the same subshell of orbitals.

Within the quantum level n = 5, rank the following subshells in order of increasing energy: f, p, s, d, g. Assume the atom is a multi-electron system

Order of increasing energy: 5s < 5p < 5d < 5f < 5g

Explain how Coulomb's law, shielding, and penetration determine the energy ordering of orbitals in multielectron atoms.

Penetration and its effects on shielding cause shells of orbitals to split into subshells with different energies. Electrons in orbitals that penetrate closer to the nucleus are lower in energy due to coulombic attractions than electrons in orbitals that lie on average further away from the nucleus.

What is meant by penetration?

Penetration refers to an electron's proximity to the nucleus of an atom. Along with effective nuclear charge, penetration is a phenomenon that helps explain many periodic trends.

Explain how shielding results in the effective nuclear charge experienced by electron

Shielding is the result of electron-electron repulsions in an atom. Inner electrons shield outer electrons from experience the full nuclear charge.

Describe the significance of the angular momentum quantum number.

The angular momentum quantum number (l) represents the shape of an atomic orbital, and it has allowed values ranging from 0 to n- 1. Different values of l correspond to different orbital shapes.

Describe the aufbau principle and give an example.

The aufbau principle is the building up and filling of orbitals from the lowest energy orbital to the highest energy orbital. For example, the electron configuration for lithium has a total 3 electrons. The first two electrons fill the 1s orbital, and the third electron must go into the empty 2s orbital, the next lowest energy orbital available. The resulting ground state electron configuration for lithium is 1s2 2s1.

Describe the significance of the magnetic quantum number.

The magnetic quantum number (ml) represents the orientation in space of an atomic orbital, and it has allowed values ranging from -l to +l. Additionally, the number of allowed values of ml for a given value of l gives the number of orbital orientations.

Describe the significance of the principal quantum number

The principal quantum number (n) represents the size of an atomic orbital, and it can be any positive whole number. Electrons with larger values of n have larger orbitals and higher energies, owing to greater probability of being located farther away from the nucleus.

Using the idea of penetration, justify the order of orbital filling for 1s, 2s, and 2p orbitals.

The radial probability function for a 1s orbital indicated a region of electron density closer to the nucleus than the 2s orbital, and the 2s orbital penetrates closer to the nucleus than the 2p orbital. Therefore, the 1s orbital is lowest in energy, followed by the 2sorbital, and then the 2p orbital. According to the aufbau principle, electrons fill, in order, the 1s, 2s, and 2p orbitals.

Describe the significance of ψ2.

The square of the wave function (ψ2) is proportional to the probability of finding an electron in a certain volume of space, and it represents the electron density. As the electron density increases, so does the probability of finding an electron in that volume of space.