Problem 39 - Chemistry and Chemical Reactivity

Question

A neutral atom has two electrons with \(n=1\), eight electrons with \(n=2,\) eight electrons with \(n=3,\) and two electrons with \(n=4 .\) Assuming this element is in its ground state, supply the following information: (a) atomic number (b) total number of s electrons (c) total number of \(p\) electrons (d) total number of \(d\) electrons (e) is the element a metal, metalloid, or nonmetal?

Step-by-Step Solution

Answer

(a) 20 (b) 8 (c) 12 (d) 0 (e) metal

Step 1: Determine the electron configuration

First, translate the given information into the electron configuration of the neutral atom. For \(n=1\), 2 electrons correspond to \(1s^2\).For \(n=2\), 8 electrons include \(2s^2\) and \(2p^6\).For \(n=3\), 8 electrons cover \(3s^2\) and \(3p^6\).For \(n=4\), 2 electrons are \(4s^2\).Thus, the full electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\).

Step 2: Find the atomic number

The atomic number is equal to the total number of electrons (since the atom is neutral). Add up all the electrons: \(2 + 8 + 8 + 2 = 20\). Thus, the atomic number is 20.

Step 3: Calculate the total number of s electrons

Identify the s subshells in the electron configuration: \(1s^2\), \(2s^2\), \(3s^2\), and \(4s^2\). Add up the electrons in these subshells: \(2 + 2 + 2 + 2 = 8\). So, there are 8 s electrons.

Step 4: Calculate the total number of p electrons

Identify the p subshells in the configuration: \(2p^6\) and \(3p^6\). Add these up: \(6 + 6 = 12\). Thus, there are 12 p electrons.

Step 5: Determine the total number of d electrons

In the given electron configuration, there are no d subshells listed (no electrons in \(3d, 4d,\) etc.). Therefore, there are 0 d electrons.

Step 6: Classify the element as a metal, metalloid, or nonmetal

An atomic number of 20 corresponds to the element calcium, which is in group 2 (alkaline earth metals) of the periodic table, making it a metal.

Key Concepts

Understanding the Atomic Number

The atomic number of an element plays a crucial role in identifying its identity and position on the periodic table. Each element on the periodic table is defined by its atomic number, which represents the number of protons in the nucleus. In a neutral atom, this is also equal to the number of electrons since the charges must balance out.
In the example problem, we calculated the atomic number by adding up all the electrons in the neutral atom. The total came to 20, meaning this atom has 20 protons and 20 electrons. Knowing the atomic number allows us to find the element’s position on the periodic table easily. Here, an atomic number of 20 identifies the element as calcium.

Core Concept: s Electrons

The 's electrons' refer to electrons in the s subshell, which is one of the simplest subshell types. The s subshell can hold a maximum of 2 electrons and has a spherical shape. It appears in every principal energy level. For the given configuration, we listed the s electrons as follows:

• For n=1: \(1s^2\)
• For n=2: \(2s^2\)
• For n=3: \(3s^2\)
• For n=4: \(4s^2\)

Adding these together, the total number of electrons that occupy s orbitals is 8. Always remember that the count of s electrons is vital as it helps determine several chemical properties and reactivity of an element.

The Role of p Electrons in Electron Configuration

p electrons occupy the p subshell, which can house a maximum of 6 electrons. The p orbital has a dumbbell shape and exists starting from the second energy level, higher than the s orbitals. In the given problem, this is how the p electrons were distributed:

• For n=2: \(2p^6\)
• For n=3: \(3p^6\)

Summing them yields 12 p electrons in total. These electrons are crucial for elements known as nonmetals and are predominantly responsible for an atom's ability to form covalent bonds.

Periodic Table Classification: Metal, Metalloid, or Nonmetal

Understanding how an element is classified on the periodic table helps predict its characteristics. The periodic table divides elements into metals, metalloids, and nonmetals based on their properties. In this exercise, we looked at the atomic number 20, which correlates with calcium on the periodic table. Calcium is found in Group 2, known as the alkaline earth metals. These elements are classified as metals. Metals typically have these properties:

• Good conductors of electricity and heat
• Malleable and ductile
• High melting and boiling points

Knowing these traits allows us to make educated guesses about the element's behavior in various reactions and conditions, confirming that calcium exhibits typical metallic properties.