Quantum Mechanics
What principle states that each orbital can hold, at most, two electrons with opposite spins?
Pauli Exclusion Principle
Write the electron configuration for a neutral atom of chlorine.
1s² 2s² 2p⁶ 3s² 3p⁵
What is the maximum number of electrons in a p sublevel?
6
3x108 m/s
What happens to an electron when an atom absorbs energy?
It moves to a higher energy orbital (excited state).
What rule explains why electrons enter orbitals of lowest energy first?
Aufbau Principle
Which sublevel fills before the 3d sublevel starts filling?
4s
How many orbitals are in the d sublevel?
5
Which quantum leap emits the greatest energy photon: n = 5 → n = 1 or n = 4 → n = 2?
n = 5 → n = 1
What do the discrete lines in atomic emission spectra represent?
Electrons drop from higher to lower energy levels, emitting photons of specific energies. Each line represents a specific electron transition within the atom.
Which principle states that it is impossible to know both the position and velocity of an electron simultaneously?
Heisenberg Uncertainty Principle
Write the full electron configuration for a neutral oxygen atom AND state how many electrons are in the highest energy level.
1s² 2s² 2p⁴ → 6 electrons in the highest energy level (n=2).
Which orbital type has a dumbbell shape?
p orbitals/sublevels
State the relationship between frequency, energy, and wavelength.
As frequency increases, energy increases and wavelength decreases.
Frequency and Energy are directly related, wavelength is inversely related to both.
Potassium produces a lilac flame (~766 nm) while calcium produces a bright orange flame (~622 nm). Which flame color is associated with higher energy?
Calcium (622 nm) → shorter wavelength → higher energy than potassium (766 nm).
What is meant by ground state?
n=1 or the lowest energy arrangement of electrons in an atom.
Sulfur has 16 electrons. Write the electron configuration and explain why Hund’s rule is used when filling the 3p orbitals.
1s² 2s² 2p⁶ 3s² 3p⁴
Hund’s rule: electrons occupy degenerate 3p orbitals singly before pairing to minimize electron-electron repulsion and increase stability.
If four electrons occupy orbitals in the 3p sublevel, how are they distributed according to Hund’s rule? (draw a picture)
First orbital will have two electrons with opposite spins. The next two orbitals will each have one electron with parallel spins.
A gamma ray has a frequency of 2.73 × 10²⁰ Hz. What is its wavelength? (c = 3.00 × 10⁸ m/s)
λ = c/ν
1.10 × 10⁻¹² m
Describe the difference between the Bohr model and the quantum mechanical model of the atom.
Bohr model: electrons in fixed orbits; Quantum model: electrons in probabilistic clouds (orbitals) and energy sublevels.
In a hydrogen atom, the energy difference between lower levels (like n = 1 and n = 2) is bigger than the difference between higher levels (like n = 5 and n = 6). How does this difference in energy affect the color of light that is emitted when electrons fall between these levels?
Lower levels (n = 1 → 2) have bigger energy differences → electrons release higher-energy photons → shorter wavelength light → blue/violet.
Higher levels (n = 5 → 6) have smaller energy differences → electrons release lower-energy photons → longer wavelength light → red.
A calcium atom (20 electrons) is in an excited state where one 4s electron is promoted to 3d. Write the electron configuration and explain why this excited state has higher energy than the ground state.
Answer: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹ 4s¹
Explanation: Energy is absorbed to move an electron to a higher orbital; excited state is less stable than the ground state because electrons occupy higher-energy orbitals.
The following is given as the electron configuration for Chromium:
1s² 2s3 2p⁶ 3s² 3p⁶ 4p² 3d34s²
Identify all 3 errors in this electron configuration.
1. 2s3
2. 4p2 should not fill before 3d or 4s
3. Incorrect number of electrons-- Cr should have 24
Ultraviolet light has a wavelength of 2.94 × 10⁻⁸ m. Calculate:
Its frequency
The energy of a single photon
(c = 3.00 × 10⁸ m/s, h = 6.63 × 10⁻³⁴ J·s)
ν = c/λ = (3.00 × 10⁸)/(2.94 × 10⁻⁸) ≈ 1.02 × 10¹⁶ Hz
E = hν = (6.63 × 10⁻³⁴)(1.02 × 10¹⁶) ≈ 6.76 × 10⁻¹⁸ J
Explain why atomic emission spectra consist of discrete lines rather than a continuous spectrum.
Electrons occupy discrete energy levels; photons emitted correspond to specific energy differences, producing discrete spectral lines.