Chapter U1.24, Problem 9E

Interpretation Introduction

(a)

Interpretation:

The electronic configuration of the element with atomic number 13 needs to be identified.

Concept introduction:

The electronic configuration of an element is the distribution of the electrons in an atom of the element into atomic orbitals. It is known that the atomic orbitals are designated as 1s, 2s, 2p, 3s, etc depending on their energy and distance from the nucleus. These atomic orbitals accommodate the electrons orbiting around the nucleus.

Answer to Problem 9E

The electronic configuration of the element with atomic number 13 is 1s²2s²2p⁶3s²3p¹

Explanation of Solution

The atomic orbital closest to the nucleus is the 1s orbital followed by the 2s orbital, then 2p and so on. Each electronic orbital can hold maximum 2 electrons. Thus, both the 1s and 2s orbitals can hold 2 electrons each. There are 3 p orbitals depending on their orientations with respect to the nucleus and each p orbital can hold 2 electrons at maximum. Thus, the 2p and 3p orbitals can accommodate 6 electrons in total.

The energy of the orbitals is guided by the principal quantum number, n of the orbital. The orbital having n = 1 has the lowest energy (closest to the nucleus) and the energy of the orbitals increases with increasing n values.

Further, while filling up the atomic orbitals, it must be noted that unless a lower energy atomic orbital is completely filled with electrons, the next higher energy orbital will not be filled up with an electron.

The element with atomic number 13 has 13 electrons in total (the atomic number is equal to the number of electrons contained in the neutral atom). The first two electrons must go in the 1s orbital followed by 2 electrons in the 2s orbital. The next available orbital is the 2p orbital which can hold 6 electrons. The remaining 3 electrons go into the 3s and 3p orbitals. This will give the electronic configuration stated above (the superscripts denote the number of electrons in the atomic orbitals).

Interpretation Introduction

(b)

Interpretation:

The number of valence electrons in the element with atomic number 13 needs to be determined.

Concept introduction:

The valence electrons are defined as the electron occurring in the outermost, highest energy orbitals of the element. Since a principal shell (defined by quantum number n) can have more than 1 sub-shell or atomic orbital, hence, all the electrons occurring in the highest shell are considered as valence electrons.

Answer to Problem 9E

The number of valence electrons in the element with atomic number 13 is 3.

Explanation of Solution

It has already been stated above that the highest energy shell in the element with atomic number 13 is the third shell (n = 3). Since the third shell has three available atomic orbitals (s, p and d) out of which the s and the p orbitals are occupied here, hence, the sum total of the electrons in the third shell is the number of valence electrons in the element.

Interpretation Introduction

(c)

Interpretation:

The number of core electrons in the element with atomic number 13 needs to be determined.

Concept introduction:

The core electrons are defined as the electrons occurring in the inner, lower energy orbitals of the element. Since a principal shell (defined by quantum number n) can have more than 1 sub-shell or atomic orbital, hence, all the electrons occurring in the inner shells are considered as core electrons.

Answer to Problem 9E

The number of core electrons in the element with atomic number 13 is 10.

Explanation of Solution

The valence electrons of the element having atomic number 13 occur in the third shell and there are 3 valence electrons. Thus, the remaining electrons must be the core electrons and a simple subtraction determines the number of core electrons as 10.