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Quantum numbers
Quantum numbers
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28 Terms
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1
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What are quantum numbers?
A set of four values that describe the unique position, energy, and spin of each electron in an atom.
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What do quantum numbers represent?
They define the energy level, shape, orientation, and spin of an electron’s orbital.
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List the four quantum numbers.
n (principal), ℓ (angular momentum), mₗ (magnetic), mₛ (spin).
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What does the principal quantum number (n) describe?
The energy level and size of the orbital; larger n means higher energy and larger orbital.
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What are the allowed values for n?
Positive integers: 1, 2, 3, 4, …
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How does the value of n relate to orbital energy?
As n increases, orbital energy and average distance from the nucleus increase.
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What does the angular momentum quantum number (ℓ) describe?
The shape of the orbital (spherical, dumbbell, cloverleaf, etc.).
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What are the possible values of ℓ for a given n?
ℓ ranges from 0 to (n − 1).
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What letter corresponds to each ℓ value?
ℓ = 0 → s, ℓ = 1 → p, ℓ = 2 → d, ℓ = 3 → f.
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How many sublevels are in each energy level?
The number of sublevels equals the value of n.
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What does the magnetic quantum number (mₗ) describe?
The orientation of the orbital in 3D space around the nucleus.
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What are the allowed values of mₗ?
All integers from −ℓ to +ℓ, including 0.
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How many orbitals are in each sublevel?
Number of orbitals = 2ℓ + 1.
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What does the spin quantum number (mₛ) describe?
The direction of an electron’s spin in an orbital.
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What are the possible values of mₛ?
+½ (spin-up) and −½ (spin-down).
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How many electrons can fit in one orbital?
Two electrons with opposite spins.
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What does the Pauli Exclusion Principle state?
No two electrons in an atom can have the same four quantum numbers.
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What does Hund’s Rule state?
Electrons fill degenerate orbitals singly with parallel spins before pairing.
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What does it mean if orbitals are degenerate?
They have the same energy level (e.g., the three 2p orbitals).
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What is an atomic orbital?
A region in space where there is a high probability of finding an electron.
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What is an orbital node?
A region where the probability of finding an electron is zero.
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What are the two types of nodes?
Radial (spherical) and angular (planar).
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How do you calculate the number of radial nodes?
Radial nodes = n − ℓ − 1.
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How do you calculate the total number of nodes in an orbital?
Total nodes = n − 1.
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How do you calculate the number of angular nodes?
Angular nodes = ℓ.
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What does orbital phase refer to?
The sign (+ or −) of the wave function; it changes across a node.
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Which quantum numbers determine the energy of an orbital in multi-electron atoms?
Both n and ℓ (since electron–electron repulsion affects energy).
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How does the periodic table reflect quantum numbers?
s-block (ℓ=0), p-block (ℓ=1), d-block (ℓ=2), f-block (ℓ=3).