Electrons in Atoms, Quantum Mechanics, and Light

Flashcards covering the Bohr model, Schrödinger's quantum mechanical model, sublevels and orbital shapes, electron configurations (Aufbau principle, Pauli exclusion principle, Hund's rule), wave mechanics, and atomic emission spectra.

Who developed the quantum mechanical model of the atom?

Erwin Schrödinger (1887–1961).

How does the quantum mechanical model define an orbital?

An orbital is defined as a region of space with a high probability of finding an electron.

What characteristics of an orbital are determined by the principal quantum number ($n$)?

The principal quantum number ($n$) determines the size of the orbital, its distance from the nucleus, and its energy level.

What did Niels Bohr propose about electron orbits and energy in 1913?

Bohr proposed that electrons move only in specific circular paths (orbits) around the nucleus and possess a fixed amount of energy (a quantum of energy).

What limitation did the Rutherford atomic model have regarding electron behavior?

It could not explain the chemical properties of elements or why heated objects emit specific colors of light.

For which element did the Bohr model successfully explain experimental results, and where did it fail?

It successfully explained the results for the hydrogen atom, but failed to explain the properties and spectra of atoms with more than one electron.

Which sublevels are present in principal energy levels $n = 1$, $n = 2$, $n = 3$, and $n = 4$?

$n = 1$ has $1s$; $n = 2$ has $2s, 2p$; $n = 3$ has $3s, 3p, 3d$; and $n = 4$ has $4s, 4p, 4d, 4f$.

How many individual orbital orientations exist for $p$, $d$, and $f$ sublevels?

The $p$ sublevel has $3$ types ($p_x, p_y, p_z$), the $d$ sublevel has $5$ types, and the $f$ sublevel has $7$ types.

What mathematical formula gives the maximum number of electrons that can occupy a principal energy level ($n$)?

$$2n^2$$

What is the maximum number of electrons allowed in energy levels $n = 1$, $n = 2$, $n = 3$, and $n = 4$?

$n = 1$ holds $2$ electrons; $n = 2$ holds $8$ electrons; $n = 3$ holds $18$ electrons; and $n = 4$ holds $32$ electrons.

What geometrical shapes correspond to $s$ and $p$ orbitals?

An $s$ orbital is spherical, whereas $p$ orbitals are dumbbell-shaped.

What is meant by a ground state electron configuration?

It is the lowest-energy, most stable arrangement of electrons in an atom.

What does the Aufbau principle dictate when writing electron configurations?

Electrons must occupy the lowest-energy orbitals first.

What restriction does the Pauli exclusion principle place on electrons in an orbital?

It limits the number of electrons in an orbital to two ($2$), and they must have opposite spins.

How are positive and negative electron spins represented in orbital diagrams?

An up arrow represents positive spin ("spin up"), and a down arrow represents negative spin ("spin down").

What rule governs the filling of degenerate orbitals ($p$, $d$, $f$) according to Hund's rule?

Electrons occupy orbitals of equal energy singly with parallel spins first to minimize electron repulsion, pairing up only when necessary.

What is wavelength ($\lambda$) and what units are used to measure it?

Wavelength is the distance between identical points on consecutive waves, measured in units of meters ($\text{m}$).

What is frequency ($\nu$) and what units are used to quantify it?

Frequency is the number of times a wave cycle repeats in a given time, measured in Hertz ($\text{Hz}$).

What mathematical relationship links wavelength ($\lambda$), frequency ($\nu$), and the speed of light ($c$)?

$\lambda \nu = c$, where the speed of light $c = 3.00 \times 10^8\,\text{m/s}$.

How are wavelength ($\lambda$) and frequency ($\nu$) related to one another?

Wavelength and frequency are inversely proportional.

How do atoms produce atomic emission spectra?

When atoms absorb energy, their electrons move to higher energy levels; when they return to lower energy levels, they lose energy by emitting light.

Why is the atomic emission spectrum useful for identifying an element?

The atomic emission spectrum of each element is unique to that element.