Chapter 5, Problem 34A

(a)

Interpretation Introduction

Interpretation: The number of sublevels in principal energy level 1 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

For the given principal quantum number (n), the azimuthal quantum number can be calculated as follows:

  $l=0,\text{ 1, 2,}\mathrm{.....}n-1$

Since the principal quantum number is given 1, the value $n-1$ will be:

  $\begin{array}{c}n-1=1-1\\ =0\end{array}$

Thus, $l=0$

There is only 1 value for an azimuthal quantum number, which is 1.

Thus, there is only 1 subshell in principal energy level 1 that is s subshell.

(b)

Interpretation Introduction

Interpretation: The number of sublevels in principal energy level 2 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

For the given principal quantum number (n), the azimuthal quantum number can be calculated as follows:

  $l=0,\text{ 1, 2,}\mathrm{.....}n-1$

Since the principal quantum number is given 2, the value $n-1$ will be:

  $\begin{array}{c}n-1=2-1\\ =1\end{array}$

Thus, $l=0,\text{1}$

There are two values for an azimuthal quantum number that is 0 and 1.

Thus, there are two subshells in principal energy level 2 that is s and p subshells.

(c)

Interpretation Introduction

Interpretation: The number of sublevels in principal energy level 3 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

For the given principal quantum number (n), the azimuthal quantum number can be calculated as follows:

  $l=0,\text{ 1, 2,}\mathrm{.....}n-1$

Since the principal quantum number is given 3, the value $n-1$ will be:

  $\begin{array}{c}n-1=3-1\\ =2\end{array}$

Thus, $l=0,\text{ 1, 2}$

There are two values for an azimuthal quantum number that is 0, 1, and 2.

Thus, there are three subshells in principal energy level 3 that is s , p, and d subshell.

(d)

Interpretation Introduction

Interpretation: The number of sublevels in principal energy level 4 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

For the given principal quantum number (n), the azimuthal quantum number can be calculated as follows:

  $l=0,\text{ 1, 2,}\mathrm{.....}n-1$

Since the principal quantum number is given 4, the value $n-1$ will be:

  $\begin{array}{c}n-1=4-1\\ =3\end{array}$

Thus, $l=0,\text{ 1, 2, 3}$

There are four values for an azimuthal quantum number that is 0, 1, 2, and 3.

Thus, there are four subshells in principal energy level 4 that is s , p , d, and f subshells.