Problem 107 - Chemistry: An Atoms-Focused Approach

Question

In which subshell are the highest-energy electrons in a ground-state atom of the isotope \(^{131}\) I? Are the electron configurations of \(^{131} \mathrm{I}\) and \(^{127} \mathrm{I}\) the same?

Step-by-Step Solution

Answer

Are the electron configurations of ^131 I and ^127 I the same? Answer: The highest-energy electrons in a ground-state atom of the isotope ^131 I are in the 5p subshell. Yes, the electron configurations of ^131 I and ^127 I are the same.

Step 1: Find the atomic number of Iodine (I) and use it to find the electron configuration

The isotope notation gives us the mass number (A) of the isotope, such as \(^{131} \mathrm{I}\). However, to find the electron configuration, we need the atomic number (Z), which represents the number of electrons in a neutral atom. Looking at the periodic table, we find that iodine (I) has an atomic number (Z) of 53. Now, we can determine the electron configuration by filling the 53 electrons into the orbitals following two rules: 1. Aufbau principle: fill electrons into orbitals in the order of increasing energy (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p) 2. Pauli exclusion principle: at most, two electrons can occupy a single orbital

Step 2: Electron configuration of iodine (I)

Using the rules mentioned in Step 1, the electron configuration of iodine with atomic number 53 can be written as: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{5} \]

Step 3: Identifying the highest-energy subshell

Referring to the electron configuration obtained in Step 2, it is evident that the highest-energy subshell is the one with the largest quantum number (n). In this case, it's the 5p subshell.

Step 4: Comparing the electron configurations for \(^{131}\mathrm{I}\) and \(^{127}\mathrm{I}\)

Since isotopes only differ in the number of neutrons and do not affect the electron configuration, the electron configurations of \(^{131} \mathrm{I}\) and \(^{127} \mathrm{I}\) are the same as both isotopes have the same atomic number (Z = 53). The electron configurations for both isotopes are: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{5} \] Therefore, the highest-energy electrons are in the 5p subshell, and the electron configurations of the isotopes \(^{131} \mathrm{I}\) and \(^{127} \mathrm{I}\) are the same.

Key Concepts

Isotopes

Isotopes are variants of a particular chemical element that share the same number of protons but have different numbers of neutrons. This difference in neutron number means isotopes of an element have different mass numbers, indicated in their notation as - For example, iodine has isotopes such as \(^{131}\mathrm{I}\) and \(^{127}\mathrm{I}\).- Both these isotopes have 53 protons since the atomic number of iodine (I) is 53. The distinct properties of isotopes, such as their stability, radioactivity, and physical characteristics, arise from these variations in neutron count. However, isotopes do not influence the electron configuration of an atom. This means that while isotopes may have varying mass numbers due to extra or fewer neutrons, the arrangement of electrons around the nucleus remains consistent as they share the same atomic number.

Highest-Energy Subshell

To determine the highest-energy subshell of an atom, we analyze its electron configuration. The subshell with the largest principal quantum number \(n\) and the highest energy level has the highest energy among the possible subshells.In the context of iodine (I), which has an atomic number of 53, its ground-state electron configuration is \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{5} \]Breaking this down: - We see that the electrons fill orbitals in increasing order of energy due to the Aufbau principle. - The 5p subshell is the highest-energy subshell as the electrons occupy orbitals from lower to higher energy levels progressively, and the 5p subshell holds the last set of electrons with \(n = 5\). Understanding electron configurations and highest-energy subshells is crucial in chemical bonding and reactions, as these electrons are often the ones involved in forming chemical bonds.

Atomic Number

The atomic number, denoted as \(Z\), is a fundamental property of an element. It corresponds to the number of protons in an atom's nucleus and defines the chemical identity of the element.- For iodine (I), the atomic number is 53.- This value indicates that a neutral iodine atom has 53 electrons, complementing the 53 protons in its nucleus.The importance of atomic numbers can be highlighted as:- Atomic numbers determine an element's position on the periodic table.- They dictate the electron configuration of an atom, influencing its chemical behavior and properties. In summary, while elements may have different isotopes, their atomic number stays fixed, continuously dictating their electron arrangement and ensuring they exhibit the characteristics of that specific element.