ELE_IC Principles of Quantum Mechanics / Atomic Orbitals

quantum numbers

The allowed energy states of atoms and molecules can be described by sets of numbers called?

Schrödinger, Heisenberg, and Dirac equations

Quantum number of the solutions of (3) equations.

4

How many quantum numbers are necessary to describe energy states of electrons in atoms?

Principle quantum number (n)

This quantum number denotes size and energy of the orbital.

Angular momentum quantum number (l)

This quantum number denotes the shape of atomic orbitals (sometimes called a subshell).

Magnetic quantum number (m_l)

This quantum number denotes the orientation of the orbital in space relative to the other orbitals in the atom.

m_l is equal to:

1s = 0 with 2 electrons

What is the magnetic quantum number if n = 1? How many electrons in total?

m_l is equal to:

2s = 0 with 2 electrons
2p = -1, 0, +1 with 6 electrons

TOTAL: 8 electrons

What is the magnetic quantum number if n = 2? How many electrons in total?

m_l is equal to:

3s = 0 with 2 electrons
3p = -1, 0, +1 with 6 electrons
3d = -2, -1, 0, +1, +2 with 10 electrons

TOTAL: 18 electrons

What is the magnetic quantum number if n = 3? How many electrons in total?

Electron spin quantum number (m_s)

This quantum number has a value that can either be -1/2 or +1/2.

Pauli exclusion principle

This principle states that in a given atom, no 2 electrons can have the same set of 4 quantum numbers.

True.

An orbital can hold only 2 electrons, and they must have opposite spins.

T or F?

symmetric

The potential energy of an electron in the field of a nucleus is spherically (asymmetric, symmetric) meaning it is proportional to Z/r and independent of orientation relative to the nucleus.

z = r cosθ

r = radius
θ = colatitude

What is the formula for z in an atomic orbital?

y = r sinθ sinΦ

r = radius
θ = colatitude
Φ = azimuth

What is the formula for y in an atomic orbital?

x = r sinθ cosΦ

r = radius
θ = colatitude
Φ = azimuth

What is the formula for x in an atomic orbital?

angular functions (θ and Φ)

The _______ determine how the probability changes from point to point at a given distance from the center of the atom; in other words, they give shape of the orbitals and their orientation in space.

radial function R

The ________ describes electron density at different distances from the nucleus.

radial distribution function, 4πr^2R(r)^2

The ______ allows us to imagine the region of space in which the electron can be found.

nodes

The positions where either component of the wave function passes through 0 are called __________>

Radial nodes

This type of node occurs where the radial component of the wave function passes through 0.

Angular nodes

This type of node occurs where the angular component of the wave function passes through 0.

increases

In all the radial probability plots, the electron density, or probability of finding the electron, falls of rapidly beyond its maximum as the distance from the nucleus (increases, decreases).

False. An electron will not be found anywhere on a nodal plane.

An electron can still be found on a nodal plane.

T or F?

52.9 pm

What is the value of the Bohr radius (a_0)?