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# Which of the following is a valid set of quantum numbers for an electron in a hydrogen atom? (a) n = 1, ℓ = 0, m ℓ = 0, m s = 1 (b) n = 1, ℓ = 1, m ℓ = 0, m s = −1/2 (c) n = 1, ℓ = 0, m ℓ = 1, m s = + 1/2 (d) n = 1, ℓ = 0, m ℓ = 0, m s = − 1/2

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### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

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Section
BuyFindarrow_forward

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 6.7, Problem 1RC
Textbook Problem
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## Which of the following is a valid set of quantum numbers for an electron in a hydrogen atom? (a) n = 1, ℓ = 0, mℓ = 0, ms = 1 (b) n = 1, ℓ = 1, mℓ = 0, ms = −1/2 (c) n = 1, ℓ = 0, mℓ = 1, ms = + 1/2 (d) n = 1, ℓ = 0, mℓ = 0, ms  = − 1/2

Interpretation Introduction

Interpretation: The valid set of quantum numbers for an electron in a hydrogen atom is to be determined from the given option.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

### Explanation of Solution

Reason for correct option

Hydrogen atom only has one electron which occupies in the 1s orbital. The values of l when the principal quantum number is n are from 0 to (n1) . Each value indicates subshell. The values of ml when the orbital angular quantum number is l are from l to +l . The principal quantum number is n=1 . Each value of l indicates subshell. For d subshell , l=0 . The possible values of ml are, ml=0 . The value of ms indicates the spin of the electron and is always either 1/2 or +1/2 . Hence, the valid set of quantum numbers for an electron in a hydrogen atom is n=1,l=0,ml=0,ms=1/2 .

Hence the correct option for the valid set of quantum numbers for an electron in a hydrogen atom is option d.

Reasons for incorrect options:

Write all the given types of the set of quantum numbers in the options except option d

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