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Unit 6: Electronic Structure and Periodic Properties

From a glowing filament's spectrum to the Schrodinger equation's probability clouds, and how the resulting shell structure writes the entire periodic table.

13 topics · 50 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

6.1 Electromagnetic Radiation and the Wave Model of Light

  1. How it worksHow do wavelength and frequency trade off against each other while the speed of light stays exactly fixed?
  2. Worked exampleFind the frequency of red light that has a wavelength of 700 nm.
  3. Common mistakeWhy isn't a light wave's amplitude related to its frequency the way its wavelength is?
  4. Going furtherWhat happens to a photon's energy as its wavelength shrinks from radio waves down to gamma rays?
Your turn1 of 2
Find the frequency of light with a wavelength of 609 nm (speed of light = 3.00 times 108 m/s).

6.1 Quantization of Energy and Planck's Hypothesis

  1. How it worksHow does Planck's idea that energy comes in discrete packets fix the runaway prediction classical physics made for blackbody radiation?
  2. Worked exampleFind the energy of a single photon of light with a frequency of 6.0 times 1014 Hz using Planck's constant.
  3. Common mistakeWhy isn't energy quantization the same as saying light is made only of particles with no wave behavior at all?
Your turn1 of 2
Find the energy of a single photon of light with a frequency of 14 times 1014 Hz (Planck's constant = 6.626 times 10−34 J times s).

6.1 The Photoelectric Effect

  1. How it worksHow does treating light as photons, each carrying a fixed energy, explain why frequency and not intensity decides whether electrons fly off?
  2. Worked exampleFind the kinetic energy of an ejected electron when light of frequency 9.0 times 1014 Hz hits a metal with a work function of 3.5 times 10−19 J.
  3. Common mistakeWhy doesn't cranking up the intensity of light below the threshold frequency ever manage to eject a single electron?
  4. Going furtherWhat happens to the number of ejected electrons, versus their kinetic energy, once you raise the light's intensity above the threshold frequency?
Your turn1 of 2
Find the kinetic energy of an ejected electron when light of frequency 16 times 1014 Hz hits a metal with a work function of 3 times 10−19 J (Planck's constant = 6.626 times 10−34 J times s).

6.2 Atomic Line Spectra and the Bohr Model

  1. How it worksHow does Bohr's idea of electrons living only in fixed circular orbits explain hydrogen's line spectrum?
  2. Worked exampleFind the wavelength of light emitted when an electron in hydrogen falls from n = 3 to n = 2.
  3. Common mistakeWhy isn't the light in an atomic emission spectrum spread out continuously the way sunlight is?
Your turn1 of 2
Find the wavelength of light emitted when an electron in a hydrogen atom falls from n = 6 to n = 2 (1/wavelength = R times (1/n22 - 1/n12), with R = 1.097 times 107 per meter).

6.2 Where the Bohr Model Succeeds and Where It Breaks Down

  1. How it worksHow does quantizing an electron's angular momentum force its orbital radius and energy to take only specific values?
  2. Worked exampleFind the energy of the electron in a hydrogen atom's n = 2 orbit using the Bohr model's energy formula.
  3. Common mistakeWhy isn't an electron in a real atom actually orbiting the nucleus the way a planet orbits the sun?
  4. Going furtherWhat happens to the Bohr model's predictions the moment you try to apply them to an atom with more than one electron?
Your turn1 of 2
Using the Bohr model's energy formula En = -2.18 times 10−18 J divided by n2, find the energy of the electron in a hydrogen atom's n = 4 orbit.

6.3 Wave-Particle Duality and the de Broglie Wavelength

  1. How it worksHow does de Broglie's equation assign every moving particle a wavelength, not just photons of light?
  2. Worked exampleFind the de Broglie wavelength of an electron moving at 2.0 times 106 m/s.
  3. Common mistakeWhy isn't a thrown baseball's wave nature ever noticeable the way an electron's is?
Your turn1 of 2
Find the de Broglie wavelength of an electron (mass 9.11 times 10−31 kg) moving at 6.42 times 106 m/s (Planck's constant = 6.626 times 10−34 J times s).

6.3 The Heisenberg Uncertainty Principle

  1. How it worksHow does trying to measure an electron's position with a photon inevitably disturb the electron's momentum?
  2. Common mistakeWhy isn't the uncertainty principle just a statement about the limits of our measuring instruments?
  3. Going furtherWhat happens to the size of the position-momentum uncertainty once the particle being measured is much heavier, like a baseball?
  4. Ties togetherHow does the uncertainty principle explain why chemists describe orbitals as probability clouds instead of fixed paths?
Your turn1 of 2
The minimum uncertainty in an electron's momentum is 35 times 10−25 kg times m/s (Planck's constant = 6.626 times 10−34 J times s). Using delta x times delta p is at least h divided by 4 π, find the minimum uncertainty in the electron's position.

6.3 The Schrodinger Equation and Atomic Orbitals

  1. How it worksHow does solving the Schrodinger equation for hydrogen produce a wave function whose square gives the probability of finding the electron?
  2. How it worksWalk me through what an orbital actually represents as a three-dimensional probability cloud around the nucleus.
  3. Common mistakeWhy isn't an orbital a path that an electron physically travels along?
  4. Going furtherWhat happens to the boundary surface drawn around an orbital as you extend it to enclose more of the total probability?
Your turn1 of 2
Chemists describe an orbital as a three-dimensional probability cloud rather than a path. Why isn't an orbital a path that an electron physically travels along?

6.3 Quantum Numbers: n, l, ml, and ms

  1. How it worksHow do the principal, angular momentum, magnetic, and spin quantum numbers each answer a different question about an electron?
  2. Worked exampleFind every allowed value of the angular momentum quantum number l for an electron with principal quantum number n = 3.
  3. Common mistakeWhy can't two electrons in the same atom ever share all four quantum numbers?
  4. Going furtherWhat happens to the number of orbitals available in a subshell as the angular momentum quantum number l climbs from 0 to 3?
Your turn1 of 2
For an electron with principal quantum number n = 5, what is the maximum allowed value of the angular momentum quantum number l?

6.3 Orbital Shapes, Nodes, and Radial Distribution Functions

  1. How it worksHow does slicing a 3D probability cloud open reveal the nodes where an electron is never found?
  2. How it worksWalk me through how a radial distribution function turns a probability density into the probability of finding the electron at a given distance.
  3. Worked exampleFind the number of radial nodes in the 3s orbital of hydrogen from its n and l values.
  4. Common mistakeWhy isn't the point of zero probability at the nucleus in a p orbital counted as a radial node?
  5. Going furtherWhat happens to an orbital's radial distribution function as the principal quantum number n increases within the same subshell type?
Your turn1 of 2
Find the number of radial nodes in an orbital with principal quantum number n = 5 and angular momentum quantum number l = 1 (radial nodes = n - l - 1).

6.4 Electron Configurations and the Aufbau Principle

  1. How it worksHow do the Aufbau principle, Hund's rule, and the Pauli exclusion principle work together to build up an atom's electron configuration?
  2. Worked exampleFind the full electron configuration of a neutral iron atom.
  3. Common mistakeWhy does chromium's actual electron configuration break the simple filling order everyone learns first?
  4. Going furtherWhat happens to an atom's electron configuration once it loses electrons to form a transition metal cation?
Your turn1 of 2
Building up an atom's electron configuration relies on three separate rules working together. How do the Aufbau principle, Hund's rule, and the Pauli exclusion principle each contribute?