Electron Structure of Atoms: Schrödinger's Model

Flashcards covering key concepts from the lecture on Electron Structure of Atoms: Schrödinger's Model, including comparisons with Bohr's model, wave functions, Schrödinger's equation, and spherical harmonics.

Bohr's model does not explain why the energies and radii can only have specific __.

values

Bohr's model does not explain orbit shapes, implying they might not always be __.

circular

Lecture 3 introduces __'s model, which complements and explains Bohr's model.

Schrödinger

In Bohr's model, electrons are considered __.

points

In Schrödinger's model, electrons are considered __.

clouds

In Bohr's model, the electron's position and momentum are precisely __.

known

In Schrödinger's model, only the __ of an electron's position and momentum are known.

averages

The __ of an electron is a function of the space variable r describing the state of the electron.

wave function

The square modulus of the wave function, ρ(r) = |ψ(r)|², gives the __ density.

probability

The property that the total probability equals 1 (that is, 100%) is known as the __ condition.

normalization

A __ is a type of wave function describing an electron around an average location r₀ with a given spread σ₀.

wave packet

The Schrödinger’s equation enables one to compute the possible __ of an electron in any given potential field.

energies

The Schrödinger’s equation reads: − ℏ2/2me ∇²ψ(r) + v(r)ψ(r) = __.

Eψ(r)

The reduced Planck’s constant (ℏ) is defined as __.

h/(2π)

For an electron in ¹H, the potential field v(r) is the __ potential generated by the proton.

electrostatic

Because of the __ symmetry of the atom, the spherical coordinate system is most convenient for the Schrödinger’s equation for ¹H.

spherical

__ are angular functions Y(θ, ϕ) that are frequently encountered in science and engineering.

Spherical harmonics

For each value of the spherical harmonic order 'l', there exist __ independent solutions.

2l + 1

For spherical harmonics, the number of nodal surfaces (cones) along the polar angle θ is __.

l − |m|

For spherical harmonics, the number of nodal surfaces (planes) along the azimuthal angle φ is __.

|m|

The total number of nodal surfaces of a spherical harmonic is equal to __.

l

A spherical harmonic with l = 0 corresponds to the chemical label __.

s

A spherical harmonic with l = 1 corresponds to the chemical label __.

p

A spherical harmonic with l = 2 corresponds to the chemical label __.

d