Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 101

Chapter 6, Problem 101

Suppose that the spin quantum number, ms, could have three allowed values instead of two. How would this affect the number of elements in the first four rows of the periodic table?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

Step 1: Understand the role of the spin quantum number (m_s) in electron configuration. The spin quantum number describes the intrinsic angular momentum of an electron, and traditionally it can have two values: +1/2 or -1/2.

Step 2: Recognize that the number of elements in a period of the periodic table is determined by the number of available electron states in the atomic orbitals for that period. Each orbital can hold a maximum of two electrons with opposite spins.

Step 3: Consider how the introduction of a third spin state would affect the capacity of each orbital. With three possible spin states, each orbital could now hold three electrons instead of two.

Step 4: Calculate the new number of elements for each of the first four periods. For example, the first period has 1s orbitals, which traditionally hold 2 electrons, but with three spin states, it would hold 3 electrons, thus increasing the number of elements in that period.

Step 5: Apply this logic to the second, third, and fourth periods, considering the types and numbers of orbitals (s, p, d) available in each period, and calculate the total number of elements for each period with the new spin state configuration.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quantum Numbers

Quantum numbers are sets of numerical values that describe the unique quantum state of an electron in an atom. The four quantum numbers include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s). Each electron in an atom is characterized by these numbers, which determine its energy level, shape, orientation, and spin.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. The arrangement of electrons is governed by the Pauli Exclusion Principle, which states that no two electrons can have the same set of quantum numbers. If the spin quantum number (m_s) had three allowed values, it would allow for more electrons to occupy the same orbital, thereby altering the electron configurations of elements.

Periodic Table Structure

The periodic table is organized based on the atomic number and electron configurations of elements, which dictate their chemical properties. Each row (or period) corresponds to the filling of electron shells. If the spin quantum number had three values, it would increase the maximum number of electrons that can occupy each orbital, potentially leading to more elements in the first four rows, as more electrons could be accommodated in the same energy levels.

Recommended video:

Guided course

02:40

Periodic Table Classifications

Related Practice

Textbook Question

Consider the discussion of radial probability functions in'A Closer Look' in Section 6.6. (a) What is the differencebetween the probability density as a function of r and theradial probability function as a function of r ?

389

views

Textbook Question

As discussed in the A Closer Look box on 'Measurement and the Uncertainty Principle,' the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it?

479

views

Textbook Question

The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (a) Instruments for obtaining MRI data are typically labeled with a frequency, such as 600 MHz. In what region of the electromagnetic spectrum does a photon with this frequency belong?

Textbook Question

Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.

1418

views

Textbook Question

In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams. (a) What is the significance of the observation that the single beam splits into two beams?

415

views

Textbook Question

Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) Cl (b) Al (c) Zr (d) As (e) Sb (f) W.

573

views