Ch.7 - Quantum MechanicsWorksheetSee all chapters
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Ch.3 - Chemical Reactions
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BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
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Ch.7 - Quantum Mechanics
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Ch.23 - Transition Metals and Coordination Compounds

Solution: Suppose that, in an alternate universe, the possible values of mℓ are the integer values including 0 ranging from -ℓ-1 to ℓ+1 (instead of simply -ℓ to +ℓ). How many orbitals exist in each sublevel in

Problem

Suppose that, in an alternate universe, the possible values of m are the integer values including 0 ranging from -ℓ-1 to ℓ+1 (instead of simply -ℓ to +ℓ). How many orbitals exist in each sublevel in the alternate universe?

s sublevel

Solution

We have to determine how many orbitals would exist in s sublevel, in an alternate universe where the values of m range from -ℓ-1 to +ℓ+1.


To determine the number of orbitals, we have to first define the quantum numbers:


principal quantum number (n) → energy level in orbitals and its value could be any positive integer starting from 1.

angular momentum quantum number (ℓ) → (l) has to be at least 1 less than n, range of values from 0 up to (n-1).

magnetic quantum number (m) → range of values from -ℓ to +ℓ. In the alternate universe it will be -ℓ-1 to +ℓ+1.

spin quantum number (ms) → has two values: +½ and -½.

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