Notes
Light and energy levels
- $c = \lambda \nu$ with $c = 3.00 \times 10^8$ m/s, and $E = h\nu$ with $h = 6.626 \times 10^{-34}$ J·s.
- Short wavelength means high frequency and high energy.
- Electrons occupy fixed energy levels. Falling to a lower level emits a photon; each element has a unique line spectrum.
Electron configurations
- Sublevels hold s = 2, p = 6, d = 10, f = 14 electrons.
- Fill order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s.
- Aufbau (lowest first), Pauli (2 per orbital, opposite spins), Hund (one per orbital before pairing).
- Valence electrons are in the outermost level; for main groups, they match the group (1, 2, then 3 to 8 for groups 13 to 18).
The periodic table and trends
| Trend | Across a period (left to right) | Down a group |
|---|---|---|
| Atomic radius | decreases | increases |
| Ionization energy | increases | decreases |
| Electronegativity | increases | decreases |
- Key families: alkali metals (1), alkaline earth metals (2), transition metals (3 to 12), halogens (17), noble gases (18).
- Cations are smaller than their atoms; anions are larger.
Topics in this unit
Each topic has its own short notes and practice.
Practice
$\displaystyle \nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8}{6.00 \times 10^{-7}} = 5.00 \times 10^{14}$ Hz.
Total electrons $= 2 + 2 + 6 + 2 + 6 + 2 = 20$, which is calcium.
Nitrogen is $1s^2 2s^2 2p^3$, with $2 + 3 = 5$ electrons in level 2.
Electronegativity increases toward the upper right; oxygen is highest of these.
Radius decreases across a period, so in period 2 fluorine is smallest, then O, then N.
The colors come from specific energy drops that are unique to each element.
Free response
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Free-response question
When hydrogen gas is excited in a discharge tube, it gives off a bright red line with a wavelength of 656 nm.
(a) Calculate the frequency of this light.
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$\lambda = 656 \text{ nm} = 6.56 \times 10^{-7}$ m. $\displaystyle \nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8}{6.56 \times 10^{-7}} = 4.57 \times 10^{14}$ Hz.
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(b) Calculate the energy of one photon of this light.
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$E = h\nu = (6.626 \times 10^{-34})(4.57 \times 10^{14}) = 3.03 \times 10^{-19}$ J.
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(c) Explain why hydrogen gives off only certain colors instead of a continuous rainbow, and state whether the electron moved to a higher or lower level to make this light.
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Electrons in hydrogen can only have certain energies (energy levels). Light is emitted when an electron falls from a higher level to a lower one, and the photon's energy equals the fixed gap between the levels. Only certain gaps exist, so only certain colors appear. To emit light, the electron moved to a lower level (for this red line, from $n = 3$ to $n = 2$).
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