Question

Francium, Fr, is a radioactive element found in some uranium minerals and is formed as a result of the decay of actinium. a. What are the electron configurations of francium and its predicted most common ion? b. It has been estimated that at any one time, there is only one (1.0) ounce of francium on earth. Assuming this is true, what number of francium atoms exist on earth? c. The longest-lived isotope of francium is \({ }^{223} \mathrm{Fr}\). What is the total mass in grams of the neutrons in one atom of this isotope?

Short answer

The electron configurations of francium (Fr) and its most common ion (Fr⁺) are 1s₂ 2s₂ 2p⁶ 3s₂ 3p⁶ 4s₂ 3d¹⁰ 4p⁶ 5s₂ 4d¹⁰ 5p⁶ 6s₂ 4f¹⁴ 5d¹⁰ 6p⁶ 7s₁ and 1s₂ 2s₂ 2p⁶ 3s₂ 3p⁶ 4s₂ 3d¹⁰ 4p⁶ 5s₂ 4d¹⁰ 5p⁶ 6s₂ 4f¹⁴ 5d¹⁰ 6p⁶ 7s⁰, respectively. There are approximately \(7.65 \times 10^{22}\) francium atoms in 1 ounce. The total mass of neutrons in one atom of \({ }^{223} \mathrm{Fr}\) is ≈ \(1.372 \times 10^{-22}\) g.

Step-by-step solution

a. Electron Configurations of Francium and Its Ion

Firstly, let's figure out the electron configurations of francium (Fr). Fr has an atomic number of 87, which means it has 87 electrons. The electron configuration will be written as follows: 1s₂ 2s₂ 2p⁶ 3s₂ 3p⁶ 4s₂ 3d¹⁰ 4p⁶ 5s₂ 4d¹⁰ 5p⁶ 6s₂ 4f¹⁴ 5d¹⁰ 6p⁶ 7s₁ Now, let's predict its most common ion. Since francium is in Group 1 of the periodic table, it will most likely lose one electron and form a +1 ion (Fr⁺). The electron configuration of Fr⁺ will be: 1s₂ 2s₂ 2p⁶ 3s₂ 3p⁶ 4s₂ 3d¹⁰ 4p⁶ 5s₂ 4d¹⁰ 5p⁶ 6s₂ 4f¹⁴ 5d¹⁰ 6p⁶ 7s⁰

b. Number of Francium Atoms in 1 Ounce

To find the number of francium atoms in 1 ounce, we need to first convert the mass to grams and then use Avogadro's number. 1 ounce = 28.35 grams Fr has an atomic mass of approximately 223 grams/mol. Now let's find the number of moles of Fr in 1 ounce: Number of moles = (mass of element) / (molar mass of element) = (28.35 g Fr) / (223 g/mol Fr) = 0.127 moles Fr Using Avogadro's number (approximately \(6.022 \times 10^{23}\) particles/mol), we can convert moles to the number of atoms: Number of Francium atoms = (0.127 moles Fr) × (\(6.022 \times 10^{23}\) atoms/mol) ≈ \(7.65 \times 10^{22}\) atoms Fr

c. Total Mass of Neutrons in One Atom of \({ }^{223} \mathrm{Fr}\)

The isotope \({ }^{223}\mathrm{Fr}\) has 223 nucleons (protons + neutrons). Since Fr has an atomic number of 87, it means \({ }^{223}\mathrm{Fr}\) has 87 protons and (223 - 87) = 136 neutrons. The mass of one neutron is approximately \(1.008665 \times 10^{-24}\) grams. To find the total mass of neutrons in one atom of \({ }^{223} \mathrm{Fr}\), we multiply the number of neutrons by the mass of one neutron: Total mass of neutrons = (136 neutrons/atom) × (\(1.008665 \times 10^{-24}\) g/neutron) ≈ \(1.372 \times 10^{-22}\) g

Key concepts

Understanding Electron Configurations

Electron configurations play a crucial role in chemistry because they inform us about the arrangement of electrons around an atom. These arrangements are the result of electrons occupying the lowest energy levels available, which follows a set of principles such as the Pauli exclusion principle and Hund's rule.

The electron configuration for any element can be determined by its position on the periodic table. For francium (Fr), with an atomic number of 87, its electron configuration follows the pattern of filling orbitals from the lowest to the highest energy level. Initially, it fills the 1s orbital, moving outward through various s, p, d, and f subshells until it reaches the 7s subshell, which contains the last electron of the neutral atom. As a heavily reactive alkali metal, it readily loses one electron to form a positively charged ion (Fr+), resulting in a stable noble gas configuration.

This knowledge of electron configurations helps us predict chemical reactivity, bonding, and even the properties of materials. For example, as francium yields its outermost electron, we can predict that it behaves as a strong reducing agent in chemical reactions.

Isotopes of Francium

Isotopes are variants of an element that have the same number of protons but different numbers of neutrons. This leads to different mass numbers, which is the total count of protons and neutrons in the atomic nucleus. Francium naturally has several isotopes, all of which are radioactive, with ²²³Fr being the longest-lived.

Understanding isotopes is essential for areas such as radioactive dating, medical imaging, and nuclear energy. For francium, the various isotopes each have a unique half-life, dictating how long they can exist before decay. This half-life impacts the availability of francium on Earth and its applications. The isotope ²²³Fr, for example, is useful in studying nuclear reactions and may have potential uses in cancer treatment. The concept of isotopes also deepens our comprehension of nuclear stability and the forces at play within an atom's nucleus.

Applying Avogadro's Number

Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole, serves as a bridge between the microscopic world of atoms and the macroscopic world that we can measure and observe. It represents a key foundational concept in chemistry, allowing chemists to count individual atoms by weighing out a known mass of a substance.

For example, the estimated amount of francium on Earth can be used, along with Avogadro's number, to estimate the number of francium atoms present on our planet. The ability to convert between mass, moles, and the number of atoms facilitates many calculations in chemical reactions and stoichiometry. As with our exercise, using Avogadro's number helps us understand not just the vast amount of atoms in even a small sample of an element, but also the implications of that element's abundance or scarcity for scientific and practical endeavors.