Question

Three elements have the electron configurations 1\(s^{2} 2^{2} 2 p^{6} 3 s^{2}\) 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) , and 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} .\) The first ionization energies of these elements (not in the same order) are 0.590 , 0.999, and 0.738 MJ/mol. The atomic radii are 104, 160, and 197 pm. Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration. Complete the following table with the correct information.

Short answer

The three elements, their electron configurations, ionization energies, and atomic radii are as follows: Magnesium (Mg) with electron configuration 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\), ionization energy of 0.738 MJ/mol, and atomic radius of 160 pm; Sulfur (S) with electron configuration 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\), ionization energy of 0.999 MJ/mol, and atomic radius of 104 pm; Calcium (Ca) with electron configuration 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\), ionization energy of 0.590 MJ/mol, and atomic radius of 197 pm.

Step-by-step solution

Identify the elements based on electron configurations

To find out which element has the given electron configuration, we need to count the total number of electrons for each configuration. Then, we can use the periodic table to identify the element with that specific number of electrons. Element 1: 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\): Total number of electrons = 2+2+6+2 = 12 Hence, Element 1 is Magnesium (Mg). Element 2: 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\): Total number of electrons = 2+2+6+2+4 = 16 Hence, Element 2 is Sulfur (S). Element 3: 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\): Total number of electrons = 2+2+6+2+6+2 = 20 Hence, Element 3 is Calcium (Ca).

Match the ionization energies to the elements

The first ionization energy is the energy required to remove the most loosely held electron from a neutral atom. Ionization energy increases from left to right across a period and decreases from top to bottom in a group on the periodic table. Thus, Magnesium should have higher ionization energy than Calcium, and Sulfur should have the highest ionization energy among the three elements. So, the ionization energies are: - Mg: 0.738 MJ/mol - S: 0.999 MJ/mol - Ca: 0.590 MJ/mol

Match the atomic radii to the elements

Atomic radius generally decreases from left to right across a period and increases from top to bottom in a group on the periodic table. Thus, Magnesium should have a larger atomic radius than Sulfur, and Calcium should have the largest atomic radius among the three elements. So, the atomic radii are: - Mg: 160 pm - S: 104 pm - Ca: 197 pm Now we can complete the table with the correct information: Element | Electron Configuration | Ionization Energy (MJ/mol) | Atomic Radius (pm) ------- | ---------------------- | -------------------------- | ---------------- Mg | 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\) | 0.738 | 160 S | 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) | 0.999 | 104 Ca | 1\(s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\) | 0.590 | 197

Key concepts

Ionization Energy

Ionization energy is a crucial concept in understanding how atoms interact with one another. It refers to the minimum amount of energy required to remove the most loosely bound electron from a gaseous atom to form a cation. This process is essential in determining an element's reactivity.

Several factors influence ionization energy:

• Nuclear Charge: A higher positive charge in the nucleus often means a higher ionization energy because more energy is needed to overcome the attraction between the electrons and the nucleus.
• Electron Shielding: Inner shell electrons can shield outer electrons from the full attraction of the nucleus. More shielding means less ionization energy is required.
• Atomic Radius: Generally, the larger the atomic radius, the lower the ionization energy, since the outer electrons are farther away from the nucleus.

In the periodic table, ionization energy generally increases across a period (left to right) due to increasing nuclear charge and decreasing atomic radius. It decreases down a group (top to bottom) as atomic size increases and more electron shells are added, which increases shielding.

Atomic Radius

Understanding atomic radius is fundamental when studying the periodic trends in chemistry. The atomic radius is the distance from the nucleus of an atom to the outermost shell of electrons. It is a critical property because it influences how atoms bond and interact.

Atomic radius is affected by:

• Nuclear Charge: Stronger nuclear charge pulls electrons closer to the nucleus, reducing the atomic radius.
• Number of Electron Shells: More electron shells mean a larger atomic radius as the distance from the nucleus to the outer electrons increases.

In the periodic table, atomic radius decreases across a period (from left to right) because, with increased nuclear charge and the same number of shells, electrons are pulled closer to the nucleus. Conversely, the atomic radius increases moving down a group (from top to bottom) as additional shells elevate electron distance from the nucleus.

Periodic Table

The periodic table is a powerful tool for chemists, providing critical insights into element properties and trends. It organizes the elements in order of increasing atomic number. Elements in the same group (vertical columns) generally exhibit similar chemical properties because they have the same number of electrons in their outer shell.

Key features of the periodic table:

• Periods: Horizontal rows, where properties change progressively across.
• Groups: Vertical columns that contain elements with similar valence electron configurations and chemical properties.

The periodic table reveals patterns such as increasing ionization energy, electronegativity, and decreasing atomic radius across a period. Groups show predictable behavior: for instance, alkali metals in Group 1 are highly reactive metals, while noble gases in Group 18 are inert.