Question

Three elements have the electron configurations \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}\), \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\), and \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}\). The first ionization energies of these elements (not in the same order) are \(0.419,0.735\), and \(1.527 \mathrm{MJ} / \mathrm{mol}\). The atomic radii are \(1.60,0.98\), and \(2.35 \AA\). Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration.

Short answer

In conclusion, the elements can be identified as follows: 1. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2\) (Atomic number 12) has an ionization energy of 0.419 MJ/mol and an atomic radius of 2.35 Å. 2. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^6\) (Atomic number 18) has an ionization energy of 0.735 MJ/mol and an atomic radius of 1.60 Å. 3. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\) (Atomic number 19) has an ionization energy of 1.527 MJ/mol and an atomic radius of 0.98 Å.

Step-by-step solution

Identify atomic numbers from electron configurations

An element's electron configuration represents the distribution of its electrons in its atomic orbitals. The electron configuration in the form "n s^x p^y" shows the number of electrons 'x' in s orbital and 'y' in p orbital in the energy level 'n'. To find the atomic number, we must add up all the electrons in the given electron configurations. Element 1: \(1s^2 2s^2 2p^6 3s^2 3p^6\) Atomic number = 2 + 2 + 6 + 2 + 6 = 18 Element 2: \(1s^2 2s^2 2p^6 3s^2\) Atomic number = 2 + 2 + 6 + 2 = 12 Element 3: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\) Atomic number = 2 + 2 + 6 + 2 + 6 + 1 = 19

Arrange the elements in increasing order of atomic number

Element 1: Atomic number 12 Element 2: Atomic number 18 Element 3: Atomic number 19

Match the elements with ionization energy and atomic radius

General trends in the periodic table suggest that ionization energy increases as we move across a period from left to right, and atomic radius decreases. Using these trends, we can match the ionization energy and atomic radius to each configuration. Element 1: Lowest atomic number, so it should have the lowest ionization energy and largest atomic radius. Ionization energy: 0.419 MJ/mol Atomic radius: 2.35 Å Element 2: Middle atomic number, should have medium ionization energy and medium atomic radius. Ionization energy: 0.735 MJ/mol Atomic radius: 1.60 Å Element 3: Highest atomic number, should have the highest ionization energy and smallest atomic radius. Ionization energy: 1.527 MJ/mol Atomic radius: 0.98 Å In conclusion, the elements can be identified as follows: 1. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2\) (Atomic number 12) has an ionization energy of 0.419 MJ/mol and an atomic radius of 2.35 Å. 2. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^6\) (Atomic number 18) has an ionization energy of 0.735 MJ/mol and an atomic radius of 1.60 Å. 3. Element with electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\) (Atomic number 19) has an ionization energy of 1.527 MJ/mol and an atomic radius of 0.98 Å.

Key concepts

Electron Configuration

Understanding electron configuration is essential to grasp how elements behave chemically and physically. In its simplest form, electron configuration is the distribution of electrons among the orbitals of an atom. Each orbital can hold a specific number of electrons, and they are filled according to the Aufbau principle, which states that electrons occupy the lowest energy orbitals first. For example, the electron configuration of an element can be written as \(1s^2 2s^2 2p^6\), which tells us that there are two electrons in the 1s orbital, two in the 2s orbital, and six in the 2p orbitals. The superscript indicates the number of electrons in each orbital and the number before the 's' or 'p' represents the energy level or shell.

Knowledge of electron configurations allows us to predict an element's chemical properties, such as the type of bonds it can form, its magnetism, and how it will react with other elements. When considering electron configuration in relation to the periodic table, we observe that elements in the same group (column) typically have similar valence electron configurations, thus exhibiting similar chemical properties.

Periodic Table Trends

The periodic table is a powerful tool for scientists, offering a wealth of information about the elements based on their atomic structures and common properties. One of the key trends observed in the periodic table is that of atomic radius, which generally decreases as we move from left to right across a period. This occurs because, as the atomic number increases, more protons are added to the nucleus, attracting the electrons more strongly and pulling them closer to the nucleus.

As for ionization energy, which is the energy required to remove an electron from an atom, the trend is generally an increase across a period from left to right. This is due to a combination of the increasing nuclear charge, which holds electrons more tightly, and the decreasing atomic radius. Moreover, ionization energy also tends to decrease as we move down a group because the outer electrons are farther from the nucleus and are more easily removed due to lesser nuclear attraction.

These trends are not straightforward, as other factors like electron shielding and the stability of electron configurations can influence these properties. For instance, the first ionization energy decreases slightly from the 2nd to the 3rd period on the same group due to increased electron shielding, despite the trend of increasing ionization energy across a period. By utilizing these periodic trends, scientists can make educated predictions about an element’s behavior, reactivity, and properties.

Atomic Number Identification

Identification of elements by their atomic numbers is a fundamental principle of chemistry. The atomic number, denoted by the symbol 'Z', is unique to each element and represents the number of protons found in the nucleus of an atom. This number also determines the chemical behavior of the element because it dictates the number of electrons that will surround the nucleus in a neutral atom. Since the number of electrons dictates the element's position on the periodic table, the atomic number effectively gives an element its identity.

To find an element's atomic number, we sum the electrons found in its electron configuration. For instance, consider the electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^6\). The sum of the superscripted numbers equals 18, which is the atomic number of Argon (Ar). In a step-by-step solution of a problem in which electron configurations are involved, identifying the atomic number is often the first step, as this enables a connection to be made to the particular element and its position on the periodic table. Once this identification is made, a range of properties, such as ionization energy and atomic radius, can be predicted with reasonable accuracy based on periodic trends.