Chapter 6, Problem 68GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Answer the following questions as a summary quiz on this chapter. (a) The quantum number n describes the ________ of an atomic orbital, and the quantum number ℓ describes its ________. (b) When n = 3, the possible values of ℓ are _________. (c) What type of orbital corresponds to ℓ = 3? ________ (d) For a 4d orbital, the value of n is _______, the value of ℓ is ________, and a possible value of mℓ is _________. (e) Each of the following drawings represents a type of atomic orbital. Give the letter designation for the orbital, give its value of ℓ, and specify the number of planar nodes. Letter = ______ ______ℓ value = ______ ______Planar nodes = _______ ______ (f) An atomic orbital with three planar nodes through the nucleus is a(n) ______ orbital. (g) Which of the following orbitals cannot exist according to modem quantum theory: 2s, 3p, 2d, 3f, 5p, 6p? (h) Which of the following is not a valid set of quantum numbers? (i) What is the maximum number of orbitals that can be associated with each of the following sets of quantum numbers? (One possible answer is ″none. ″) (i) n = 2 and ℓ =1 (ii) n = 3 (iii) n = 3 and ℓ = 3 (iv) n = 2, ℓ = 1, and mℓ = 0

(a)

Interpretation Introduction

Interpretation: For an atomic orbital what does the quantum number n and l describes should be given.

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

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

Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom...

(b)

Interpretation Introduction

Interpretation: The possible values of l when n=3 should be determined.

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.

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell.

(c)

Interpretation Introduction

Interpretation: The type of orbital that corresponds to l=3 should be determined.

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.

The values of l when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell.

(d)

Interpretation Introduction

Interpretation: The value of n, l and a possible value of ml should be determined.

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.

The principal quantum number and number of subshells are same in a shell.

The values of l when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell.

The values of ml when the orbital angular quantum number is l are from l to +l.

(e)

Interpretation Introduction

Interpretation: The appropriate letters, l value and number of planar nodes should be given in the table for the given orbital pictures.

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.

The values of l when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell.

Nodal surfaces: the surface which passing through nucleus where there is zero chance of finding electrons.

(f)

Interpretation Introduction

Interpretation: The atomic orbital having three planar nodes through the nucleus should be determined.

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.

Nodal surfaces: the surface which passing through nucleus where there is zero chance of finding electrons.

The values of l when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell.

(g)

Interpretation Introduction

Interpretation: The orbitals that cannot exist according to modern quantum theory should be determined from the given orbitals.

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.

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell

(h)

Interpretation Introduction

Interpretation: The invalid set of quantum numbers should be determined from the given sets of quantum numbers.

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.

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell.

The values of ml when the orbital angular quantum number is l are from l to +l.

(i)

Interpretation Introduction

Interpretation: The maximum number of orbitals should be determined for the given set of quantum numbers.

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.

The principal quantum number and number of subshells are same in a shell.

In a subshell there are (2l+1) number of orbital.

There are n2 number of orbitals in a shell for the principal quantum number, n.

• Planck’s equation,

E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

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