Quiz 7

What is a quantum mechanical orbital?

An orbital is a probability distribution map showing where the electron is likely to be found.

List all orbitals from 1s through 5s according to increasing energy for multielectron atoms.

In order of increasing energy the orbital are 1s<2s<2p<3s<3p<4s<3d<4p<5s . The 4s orbital fills before the 3d and the 5s fills before the 4d. They are lower in energy because of greater penetration of the 4s and 5s orbitals.

What are the possible values of the magnetic momentum quantum number ml? What does the magnetic momentum quantum number determine?

The magnetic quantum number m(subscore l) is an integer ranging from -l to + l. For example if l=1 tham m(subscore l( = -1, 0, +1 The magnetic quantum number specifies the orientation of the orbital

#32 Make sketches of s, p, and d orbitals.

see book

List all the orbital in each principal level. Specify the three quantum numbers for each orbital

see table n . l . ml 1 . 0 . 0 2 . 0 . 0 1 . -1, 0, +1 3. 0 . 0 1 . -1,0, +1 2 . -2, -1, 0, +1, +2 4. 0 . 0 1 . -1,0, +1 2 . -2, -1, 0, +1, +2 3 . -3, -2, -1, 0, +1, +2, +3

Explain the contributions of Meyer and Mosely to the periodic table.

Meyer proposed an organization of the known elements based on some periodic properties. Moseley listed elements according to the atomic number rather than the atomic mass. This resolved the problems in Mendeleev's table where an increase in atomic mass did not correlate with similar properties.

What are periodic properties?

A periodic property is predictable based on the element's position within the periodic table.

What is a probability distribution map?

A probability distribution map is a statistical map that shows where an electron is likely to be found under a given set of conditions.

What is a trajectory? What kind of information do you need to predict the trajectory of a path?

A trajectory is a path that is determined by the particle's velocity (the speed and direction of travel), its position, and the forces acting on it. Both position and velocity are required to predict a trajectory.

What is an electron configuration? Give an example.

An electron configuration shows the particular orbitals that are occupied by electrons in an atom. Some examples are H=1s¹ He= 1s², and Li= 1s²2s¹

What is an orbital diagram? Provide an example.

An orbital diagram is a different way to show the electron configuration of an atom it symbolizes the electrons as an arrow in a box that represents the orbital. (Look at answers for diagram of Hydrogen)

Why are atoms usually portrayed as spheres when most orbitals are not sphere shaped.

Atoms are usually drawn as spheres because most atoms contain many electrons occupying a number of different orbitals. Therefore, the shape of atom is obtained by superimposing all of its orbitals. If the s, p, and d orbitals are superimposed they have a spherical shape.

Why does the uncertainty principle make it impossible to predict a trajectory for an electron?

Because the uncertainty principle says that you cannot know both the position and velocity of the electron simultaneously, you cannot predict the trajectory

What is penetration? How does the penetration of an orbital into the region occupied by core electrons affect the energy of an electron in that orbita;?

Penetration occurs when an electron penetrates the electron cloud of the 1s orbital and experiences the charge of the nucleus more fully because it is less shielded by the intervening electrons. As the outer electron undergoes penetration into the region occupied by the inner electrons, it experiences a greater nuclear charge and therefore, according to Coulomb's law, a lower energy.

What is shielding? In atom, which electrons tend to do the most shielding (core electrons or valence electrons)

Shielding or screening occurs when one electron is blocked from the full effects of the nuclear charge so that the electron experiences only a part of the nuclear charge. It is the inner (core electrons that shield the outer electrons from the full nuclear charge.

Why is electron spin important when writing electron configurations? Explain in terms of the Pauli exclusion principle.

The Pauli exclusion principle states the following: No two electrons in an atom can have the same four quantum numbers. Because two electrons occupying the same orbital have three identical quantum numbers (n,l, ml) they must have a different spin quantum numbers. The Pauli exclusion principle implies that each orbital can have a maximum of only two electrons, with opposing spins.

What are the possible values of the angular momentum quantum number l? What does the angular momentum quantum number determine?

The angular momentum quantum number (l) is an integer that has the possible values of 0, 1, 2, 3, and so on. The angular momentum quantum number determines the shape of the orbital. It can take values from 0 to (n-1) where n is the principal quantum number

Explain the contributions of Johann Döbereiner and John Newlands to the organization of the elements according to their properties.

The first attempt to organize the elements according to similarities in their properties was made by the German chemist Johann Döbereiner. He grouped elements into triads: three elements with similar properties. A more complex approach was attempted by English chemist John Newlands. He organized elements into octaves, analogous to musical notes. When arranged this way, the properties of every eighth element were similar.

An electron behaves in ways that are at least partially indeterminate. Explain this statement

The indeterminate behavior of an electron means that under identical conditions, the electron does not have the same trajectory and does not "land in the same spot each time.

What is the Schrödinger equation? What is a wave function? How is a wave function related to an orbital?

The mathematical derivation of energies and orbitals for electrons in atoms comes from the Schrödinger equation. The general form of the Schrödinger equation is Hγ=Eγ The symbol H stands for the Hamiltonian operator, a set of mathematical operations that represent the total energy (kinetic and potential) of the electron within the atom. The symbol E is the actual energy of the election. The symbol γ is the wave function, a mathematical function that describes the wave-like nature of the electron. A plot of the wave function γ² represents an orbital, a position probability distribution map of the electron.

Who is credited with arranging the periodic table? How are the elements arranged in the modern periodic table?

The modern periodic table is accredited to the Russian chemist Dmitri Mendeleev. Mendeleev's table is based on the periodic law, which states that when elements are arranged in order of increasing mass, their properties recur periodically. Mendeleev arranged the elements in a table in which mass increased from left to right and elements with the similar properties fell in the same columns.

The periodic table is a result of the periodic law. What observations led to the periodic law? What theory explains the underlying reasons for the periodic law.

The periodic law was based on the observations that the properties of elements recur and certain elements have similar properties. The theory that explains the existence of the periodic law is quantum mechanical theory

What are the possible values of the principal quantum number n? What does the principle quantum number determine?

The principal quantum number (n) is an integer that has has possible values of 1, 2, 3, and so on. The principal quantum number determines the overall size and energy of an orbital.

For each solution to the Schrödinger equation what can be precisely specified: the electron's energy or its position? Explain.

Using the Schrödinger equation, we describe the probability distribution maps for electron states. In these the electron has a well-defined energy, but not a well-defined position. In other words, for each state, we can specify the energy of the electron precisely but not its location at a given instant. The electron's position is described in terms of an orbital.

What is Coulomb's Law? Explain how the potential energy of two charged particles depends on the distance between the charged particles and on the magnitude and sign of their charges.

Coulomb's law states that the potential energy (E) of two charged particles depends on their charges (q₁ and q₂) and their separation (r) E=1/(4piε₀) x (q₁q₂/r) The potential energy is positive for charges of the same sign and negative for charges of the opposite sign. The magnitude of the potential energy depends inversely on the separation between the charged particles.

What are degenerate orbitals? According to Hund's Rule, how are degenerate orbitals occupied?

Degenerate orbitals are orbitals of the same energy. In a multielectron atom, the orbitals in a sublevel are degenerate. Hund's rule states that when filling degenerate orbitals, electrons fill them singly first, with parallel spins. This is a result of an atom's tendency to find the lowest energy state possible.

Newton's laws of motion are deterministic. Explain this statement.

Deterministic means that the present determines the future. That means that under the identical condition, identical results will occur.

Explain Heisenberg's uncertainty principle. What paradox is at least partially solved by the uncertainty principle?

Heisenberg's uncertainty principle states that the product of ∆x and m∆v must be greater or equal to a finite number. In other words, the more accurately you know the position of an electron (the smaller ∆x) the less accurately you can know its velocity (the bigger ∆v) and vice versa. The complementarity of the wave nature and particle nature of the electron results in the complementarity of velocity and position. Heisenberg solved the contradiction of an object as a both a particle and a wave by introducing complementarity - an electron is observed as either a particle or a wave, but never both at once.

Explain the difference between a plot showing the probability density for an orbital and one showing the radial distribution function.

The probability density is the probability per unit volume of finding the electron at a point in space. The radial distribution function represents the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus. In contrast to probability density, which has a maximum at the nucleus for an s orbital, the radial distribution function has a value of zero at the nucleus. It increases to a maximum and then decreases again with increasing r.

Which periodic property is particularly important to nerve signal transmission? Why?

The relative size of the sodium and potassium ions is important to nerve signal transmission. The pumps and channels within cell membranes are so sensitive that they can distinguish between the sizes of these two ions and selectively allow only one or the other to pass. The movement of ions is the basis for the transmission of nerve signal in the brain and throughout the body,

List the the four different sublevels. Given that only a maximum of two electrons can occupy an orbital, determine the maximum number of electrons that can exist in each sublevel.

The sublevels are s (l=0) which can hold a maximum of 2 electrons p(l=1) which can hold a maximum of 6 electrons; d(l=2) which can hold a maximum of 10 electrons and f(l=3) which can hold a maximum of 14 electrons

Why are sublevels within a principal level split into different energies for multielectron atoms but not for the hydrogen atom?

The sublevels within a principal level in multielectron atoms because of the penetration of the outer electrons into the region of the core electrons. The sublevels in hydrogen are not split because they are empty in the ground state.

What are valence electrons? Why are they so important?

Valence electrons are important in chemical bonding. For main group elements the valence electrons are in the outermost principal energy level. For transition elements, we also count the outermost d electrons among the valence, even though they are not in the outermost principal energy level. The chemical properties of an element depend on its valence electrons, which are important in bonding because they are hold most loosely. This is why the elements in a column of the periodic table have similar chemical properties: they have the same number of valence electrons.