Question

Imagine a world in which the rule for the $l$ quantum number is that values start with 1 and go up to $n$. The rules for the $n$ and $m_{l}$ quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., $n=1$ and $n=2$ ).

Name: Problem 32, Chapter 7: General Chemistry
Uploaded: 2021-06-21T20:31:44-08:00
Duration: 1 min 50 s
Channel: Lottie Adams
Description: Imagine a world in which the rule for the l quantum number is that values start with 1 and go up to n. The rules for the n and ml quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., n=1 and n=2 ).

   Imagine a world in which the rule for the $l$ quantum number is that values start with 1 and go up to $n$. The rules for the $n$ and $m_{l}$ quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., $n=1$ and $n=2$ ).

General Chemistry

Darrell Ebbing,… 9th Edition

Chapter 7, Problem 32

Instant Answer

Solved by Expert Lottie Adams

06/21/2021

Step 1

For the first shell (n=1), we have: l = 1 (since l starts at 1 and goes up to n) For l = 1, we have ml values ranging from -l to l, so ml = -1, 0, 1 So, the quantum numbers for the first shell are: (1, 1, -1), (1, 1, 0), and (1, 1, 1) Show more…

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Imagine a world in which the rule for the $l$ quantum number is that values start with 1 and go up to $n$. The rules for the $n$ and $m_{l}$ quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., $n=1$ and $n=2$ ).

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Key Concepts

Magnetic Quantum Number (m_l)

The magnetic quantum number specifies the orientation of the orbital in space, with its values ranging in integer steps from -l to +l. It contributes to the degeneracy of orbitals within a subshell, which influences how electron orbitals are distributed in three-dimensional space.

Principal Quantum Number (n)

The principal quantum number indicates the main energy level or shell of an electron within an atom. It takes positive integer values starting at 1 and largely determines the overall size and energy of the orbital.

Angular Momentum Quantum Number (l)

This quantum number determines the shape of the electron orbital. Normally, l ranges from 0 to n-1, but in the alternate scenario it starts at 1 and increases up to n. This shift alters the subdivision of energy levels into different orbital types.

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