Chapter 5.1, Problem 6LC

(a)

Interpretation Introduction

Interpretation: The number of orbitals in the 3p sublevel needs to be determined.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

The given sublevel is 3p . Here, the principal quantum number (n) is 3. For p orbital, the value of azimuthal quantum number (l) is 1. Since possible orbitals $m_l$

will be from -l to +l that is -1, 0, +1 thus, the number of orbitals will be 3. They are represented as follows:

  

(b)

Interpretation Introduction

Interpretation: The number of orbitals in the 2s sublevel needs to be determined.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here, for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

The given sublevel is 2s. Here, the principal quantum number (n) is 2. For s orbital, the value of azimuthal quantum number (l) is 0. Since possible orbitals $m_l$

will be from -l to +l which is only 0, thus, the number of orbitals will be 1. They are represented as follows:

  

(c)

Interpretation Introduction

Interpretation: The number of orbitals in the 4p sublevel needs to be determined.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

The given sublevel is 4p . Here, the principal quantum number (n) is 4. For p orbital, the value of azimuthal quantum number (l) is 1. Since possible orbitals $m_l$

will be from -l to +l that is -1, 0, +1, thus, the number of orbitals will be 3. They are represented as follows:

  

(d)

Interpretation Introduction

Interpretation: The number of orbitals in the 3d sublevel needs to be determined.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here, for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

The given sublevel is 3d . Here, the principal quantum number (n) is 3. For d orbital, the value of azimuthal quantum number (l) is 2. Since possible orbitals $m_l$ will be from -l to +l that is -2, -1, 0, +1, +2, thus, the number of orbitals will be 5. They are represented as follows:

  

(e)

Interpretation Introduction

Interpretation: The number of orbitals in the 4f sublevel needs to be determined.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here, for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Explanation of Solution

The given sublevel is 4f . Here, the principal quantum number (n) is 4. For f orbital, the value of azimuthal quantum number (l) is 3. Since possible orbitals $m_l$ will be from -l to +l that is -3, -2, -1, 0, +1, +2, +3, thus, number of orbitals will be 7. They are represented as follows: