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Questions and Answers
The mathematical expression that summarizes where an electron is likely to be found is called its ______.
wavefunction
Electrons have wavelike properties and cannot be pinpointed precisely due to the ______ uncertainty principle.
Heisenberg
Each atomic orbital is defined by three quantum numbers: principal (n), azimuthal (l), and ______ (ml).
magnetic
Electrons can have a spin of +½ for an ______ electron.
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The possible values for the spin-magnetic quantum number (ms) are +½ and ______.
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The principal quantum number (n) labels the ______ of an electron.
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The azimuthal quantum number (l) can take on values from 0 up to ______.
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Orbitals are represented by quantum numbers that define their ______.
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The values of the principal quantum number are natural numbers excluding ______.
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The four unique quantum numbers assigned to an electron are n, l, ml, and ______.
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(n – 1) __ = d-orbitals in the d-sublevel
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L = 0 (s): 2 e– in one s-orbital (ml = __)
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L = 1 (p): 2 e– in each of three p-orbitals: (px (ml = –1), py (ml = __), pz (ml = +1))
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In atoms with many electrons, electron-electron repulsions cause the energy of a d subshell (sublevel) to be higher than a s subshell of the next higher __.
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The effective nuclear charge is less than the actual charge because each electron is shielded from the full attraction of the __.
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Paired spins of two electrons are denoted __.
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All s-orbitals are __ in shape but differ in size.
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An s electron penetrates closer to the nucleus, leading to its __ in energy compared to other subshells.
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The spins of two electrons must be opposite, represented by the rational numbers +½ and __.
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Every electron in an atom must have a unique set of four __ numbers.
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Study Notes
Atomic Orbitals and Bonding
- Electrons exhibit wavelike properties.
- Heisenberg Uncertainty Principle dictates that due to an electron's wavelike nature, its precise location cannot be determined.
- The mathematical expression that describes the probability of finding an electron is called its wavefunction.
- The term "Atomic orbital" refers to the wavefunction describing the location of electrons in an atom.
- Atomic orbitals are defined by three quantum numbers:
- Principal Quantum Number (n): indicates the electron shell. Shell number corresponds to the row in the periodic table (except for d-orbitals).
- Azimuthal Quantum Number (l): indicates the subshell (s, p, d, f) and its shape.
- Magnetic Quantum Number (ml): labels specific orbitals within a subshell.
- All orbitals with the same 'n' value belong to the same shell.
- The average distance of an electron from the nucleus increases as the principal quantum number (n) increases.
Electron Spin
- Electrons possess two spin states represented as ↑ (up) and ↓ (down).
- The Spin Magnetic Quantum Number (ms) distinguishes these spin states.
- ms = +½ for an ↑ electron
- ms = –½ for a ↓ electron
Electronic Configurations – Quantum Numbers
- Every electron in an atom can be uniquely described by a set of four quantum numbers: n, l, ml, ms.
| Quantum Number | Name | Definition | Possible Values | Notes |
|---|---|---|---|---|
| n | Principal | Electron Shell | 1, 2, 3, ... | Except for d-orbitals, the shell number matches the row of the periodic table. |
| l | Azimuthal | Sublevel: s, p, d, f | 0, 1, 2, ... (n - 1) | 0 = s-orbital, 1 = p-orbitals, 2 = d-orbitals, 3 = f-orbitals |
| ml | Magnetic | Specific Orbital in a Sublevel | -l, -l + 1, ... 0, ... +l - 1, +l | l = 0 (s): 2 electrons in one orbital (ml = 0). l = 1 (p): 2 electrons in each of three orbitals (px (ml = -1), py (ml = 0), pz (ml = +1)). l = 2 (d): 2 electrons in each of five orbitals (dxy (ml = -2), dxz (ml = -1), dyz (ml = 0), dx2 - y2 (ml = +1), dz2 (ml = +2)) |
| ms | Spin | Electron Spin | +½, –½ | Electron spins must be opposite in any one orbital (paired: ↑↓). |
Orbital Energies
- In multi-electron atoms, electron-electron repulsions cause the energy of a d subshell to be higher than an s subshell of the next higher shell.
- s electrons are found closer to the nucleus compared to other electrons due to penetration.
- Each electron experiences an effective nuclear charge that is reduced due to the shielding effect of other electrons between the nucleus and the electron.
- Paired spins (↑↓) have opposite spins.
- Pauli Exclusion Principle: no two electrons in an atom can share the same set of four quantum numbers.
s-Orbitals
- s orbitals are spherical in shape.
- An electron occupying a 1s orbital is referred to as a 1s electron.
- Each shell has one s-orbital.
- Boundary surface: Represents the region around the nucleus where there is a 90% probability of finding the electron.
- All s-orbitals are spherical but differ in size: 1s < 2s < 3s.
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Description
Explore the fascinating world of atomic orbitals and their role in chemical bonding. This quiz covers essential concepts like wavefunctions, quantum numbers, and the Heisenberg Uncertainty Principle. Test your knowledge on how electrons' wavelike properties influence their location and behavior in atoms.
