Davidovits QUIZ 7 Chapter 7

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

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

7.32 Make sketches of the general shapes of the s, p, and d orbitals.

1s = circular cloud Px,Py,Pz are the bowtie shape on the different axises. D orbitals are pretty complicated.

7.23 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

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

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.

7.30 List all the orbitals in each principal level. Specify the three quantum numbers for each orbital. a.n=1 b.n=2 c. n=3 d.n=4

A) n=1 l= 0 ml = 0 B) n =2 l=0,1 ml = -1,0,1 C)n=3 l= 0,1,2 ml = -2,-1,0,1,2 D)n=4 l=0,1,2,3 ml=-3,-2,-1,0,1,2,3

7.34 Why are atoms usually portrayed as spheres when most orbitals are not spherically shaped?

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

7.25 What is a quantum-mechanical orbital?

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

7.21 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.

7.18 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 Δx and mΔv must be greater than or equal to a finite number. In other words, the more accurately you know the position of an electron (the smaller Δx), the less accurately you can know its velocity ( the bigger Δv) 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 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.

7.31 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.

7.28 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 possible values 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.

7.22 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.

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

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

7.26 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 solving the Schrödinger equation. The general form of the Schrödinger equation is HΨ = EΨ. 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 electron. A plot of the wave function squared (Ψ^2) represents an orbital, a position probability distribution map of the electron.

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

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

7.33 List 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 two 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.

7.24 For each solution to the Schrodinger 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.