Problem 63 - Chemistry An Atoms First Approach

Question

Which of the following is(are) correct? a. \(^{40} \mathrm{Ca}^{2+}\) contains 20 protons and 18 electrons. b. Rutherford created the cathode-ray tube and was the founder of the charge- to-mass ratio of an electron. c. An electron is heavier than a proton. d. The nucleus contains protons, neutrons, and electrons.

Step-by-Step Solution

Answer

The correct statement is a. \(^{40} \mathrm{Ca}^{2+}\) contains 20 protons and 18 electrons.

Step 1: Statement a: \(^{40} \mathrm{Ca}^{2+}\) contains 20 protons and 18 electrons.

The superscript 40 in \(^{40} \mathrm{Ca}\) represents the mass number, which is the sum of the number of protons and neutrons in the nucleus. Calcium (Ca) has an atomic number of 20, which means it has 20 protons. An ion with a charge of +2 indicates that the atom lost 2 electrons. Therefore, the ion has 20 - 2 = 18 electrons. So, statement a is correct.

Step 2: Statement b: Rutherford created the cathode-ray tube and was the founder of the charge-to-mass ratio of an electron.

The cathode-ray tube was not invented by Rutherford; it was invented by Sir William Crookes. Furthermore, the discovery of the charge-to-mass ratio of an electron is credited to J.J. Thomson using cathode-ray tubes. Thus, statement b is incorrect.

Step 3: Statement c: An electron is heavier than a proton.

The mass of an electron is approximately 9.11 x 10^-31 kg, while the mass of a proton is approximately 1.67 x 10^-27 kg. Therefore, an electron is much lighter than a proton, not heavier. Statement c is incorrect.

Step 4: Statement d: The nucleus contains protons, neutrons, and electrons.

The nucleus of an atom only contains protons and neutrons. Electrons, on the other hand, orbit around the nucleus at various energy levels. Statement d is incorrect. Based on our analysis, the correct statement is: a. \(^{40} \mathrm{Ca}^{2+}\) contains 20 protons and 18 electrons.

Key Concepts

Protons and Electrons

In the study of atomic structure, understanding the roles and characteristics of protons and electrons is fundamental.

• Protons are positively charged particles found within the nucleus of an atom.
• Each element is defined by its atomic number, which is the number of protons in its nucleus.
• Electrons are negatively charged and orbit around the nucleus in electron shells.

The balance between protons and electrons determines the overall charge of an atom. For instance, a neutral atom of calcium has 20 protons and 20 electrons. When it loses two electrons, it forms a cation with a +2 charge, symbolized as \(^{40} \mathrm{Ca}^{2+}\), indicating 18 electrons are present. This relationship between protons and electrons is crucial for determining the chemical behavior of an atom.

Cathode Ray Tube

The cathode ray tube (CRT) played a pivotal role in the exploration of atomic structure. Developed by Sir William Crookes, the CRT was essential in J.J. Thomson's experiments, which led to the discovery of the electron. Thomson used the CRT to investigate the electron's charge-to-mass ratio, a significant leap forward in atomic theory.

• The CRT is a vacuum tube containing a cathode, which emits electrons.
• These electrons travel towards the anode, forming a visible beam known as the cathode ray.

By manipulating this electron beam with electric and magnetic fields, Thomson was able to determine that electrons are much lighter than protons and have a negative charge. This experiment was a crucial step towards understanding the structure of the atom.

Atomic Nucleus

The atomic nucleus is the central core of an atom, housing the majority of its mass and defining its identity.

• It contains two types of subatomic particles: protons, which have a positive charge, and neutrons, which have no charge.
• The number of protons in the nucleus is what distinguishes one element from another.

Electrons, despite their presence in the atom, are not housed within the nucleus but instead orbit around it. The discovery of the nucleus was a landmark achievement in atomic theory, attributed to Ernest Rutherford's gold foil experiment. In this groundbreaking research, Rutherford demonstrated that atoms consist of a small, dense nucleus surrounded by electrons, disproving the previous "plum pudding" model that suggested electrons were dispersed throughout a positively charged sphere.

Mass of Subatomic Particles

Understanding the mass of subatomic particles is vital in grasping atomic structure.

• Protons and neutrons are significantly heavier than electrons.
• The mass of a proton is approximately \(1.67 \times 10^{-27}\) kg, and a neutron's mass is nearly the same.
• Electrons are much lighter, with a mass of about \(9.11 \times 10^{-31}\) kg.

This stark difference in mass explains why nearly all of an atom's mass is concentrated in its nucleus, where protons and neutrons reside.The understanding of these mass differences is essential when evaluating atomic stability and behavior. An electron's negligible mass contributes to the fact that it's often considered as "massless" when dealing with chemical reactions, yet it plays a critical role in defining the chemical properties of an element.