Chemistry Practice Problems Introduction to Quantum Mechanics Practice Problems Solution: Suppose that in an alternate universe, the possibl...

Solution: Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this universe and ours, how many orbitals would exist in each level in the alternate universe?n = 1

Problem

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this universe and ours, how many orbitals would exist in each level in the alternate universe?

n = 1

Solution

We have to determine how many orbitals would exist in the n=1 level, in an alternate universe where the value of ℓ is from 0 to n.


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). In the alternate universe it will be 0 → n.

magnetic quantum number (m) → range of values from -ℓ to + ℓ.

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

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