Question

An element has 24 protons in its nucleus. (a) Identify this element. (b) Write the symbol for the element's isotope. That will have a mass closest to its average atomic mass. (c) How many neutrons are in the isotope you described in part \((b) ?\) (d) How many electrons are in neutral atoms of this element? (e) How many times heavier than \({ }^{12} \mathrm{C}\) is the average atom of this element?

Short answer

The element with 24 protons is chromium (Cr). The isotope symbol for chromium with a mass closest to its average atomic mass is \(^{52}\text{Cr}\). This isotope contains \(28\) neutrons. A neutral chromium atom has \(24\) electrons. The average atom of chromium is approximately \(4.1667\) times heavier than \(^{12}\mathrm{C}\).

Step-by-step solution

Identifying the Element

The atomic number of an element is equal to the number of protons in its nucleus. The atomic number can be used to identify the element from the periodic table.

Writing the Isotope Symbol

The symbol for an isotope is written as \( ^{A}_{Z}\text{X} \), where \(A\) is the mass number (total number of protons and neutrons), \(Z\) is the atomic number (number of protons), and \(X\) is the element symbol. For the isotope with a mass closest to its average atomic mass, look at the periodic table for the element's average atomic mass and round it to the nearest whole number to find \(A\).

Calculating Neutrons in the Isotope

The number of neutrons in an isotope is given by \(A - Z\), where \(A\) is the mass number and \(Z\) is the atomic number. Using the average atomic mass rounded to the nearest whole number as \(A\) will give you the number of neutrons for the most common isotope.

Determining the Number of Electrons

In a neutral atom, the number of electrons is equal to the number of protons. Thus, the element with \(24\) protons will also have \(24\) electrons.

Comparing Average Atom Weight to Carbon-12

The average atomic mass of an element, given in atomic mass units (amu), can be compared to the mass of \(^{12}\mathrm{C}\), which is defined as \(12 \, \text{amu}\). To find out how many times heavier the average atom of the element is compared to \(^{12}\mathrm{C}\), divide the element's average atomic mass by \(12\).

Key concepts

Periodic Table

The periodic table is a comprehensive chart that organizes all the known elements according to their atomic number—that is, the number of protons in the nucleus—and other chemical properties. Elements are arranged in rows called periods and columns known as groups. This layout shows patterns in elemental characteristics, such as reactivity and metallicity, which are crucial for understanding chemical behavior. The element with 24 protons, as mentioned in the exercise, is chromium (Cr), which can be identified by its atomic number on the periodic table.

Understanding the structure of the periodic table can be empowering for students as it is the roadmap to the chemistry of elements. For example, elements in the same group often share similar properties, and as one moves from left to right across a period, the elements become less metallic in nature. The periodic table is not just a tool for classification; it is fundamental to predicting the behavior of elements in chemical reactions.

Isotopes

Isotopes are atoms of the same element that have different numbers of neutrons but the same number of protons. Because the atomic number, which depends on the number of protons, remains unchanged, isotopes of an element share chemical properties but have different atomic masses. The various isotopes of an element are represented by their mass number (A), which is the total number of protons and neutrons in the atom's nucleus.

The term 'isotope' is derived from the Greek words for 'same place,' reflecting that isotopes occupy the same position on the periodic table. Isotopes can be stable or radioactive; the stability of an isotope depends on the ratio of neutrons to protons in its nucleus. In everyday life, isotopes have applications ranging from medical imaging to the dating of archaeological artifacts.

Atomic Number

The atomic number is a fundamental property of an element and is denoted by the symbol 'Z'. It represents the number of protons in the nucleus of an atom, which also equals the number of electrons in a neutral atom. The atomic number uniquely identifies an element and determines its position on the periodic table.

As an element's atomic number increases, so does its mass and complexity. In a neutral atom, the atomic number also influences the electron configuration, which in turn affects the atom's chemical properties. For Chromium (Cr), with an atomic number of 24, this means there are 24 positively charged protons and, in a neutral state, 24 negatively charged electrons balancing the charge. It is the atomic number that students should turn to first when identifying elements or predicting their behavior in compounds and reactions.

Neutrons Calculation

Neutrons play a crucial role in the atomic structure as they contribute to the overall mass of an atom without affecting the charge. To calculate the number of neutrons in an atom's isotope, subtract the atomic number (Z) from the mass number (A). The mass number is the sum of the total number of protons and neutrons in the nucleus.

For the isotope in the given exercise, the atomic number of chromium (Cr) is 24. If we know the mass number of the most common isotope, perhaps 52, we would calculate the number of neutrons as follows: \(52 (A) - 24 (Z) = 28\) neutrons. Neutron calculation is not only essential for understanding isotopes but also for delving into nuclear chemistry and physics, where isotopes and their stability are of great importance.

Atomic Mass Units

Atomic mass units (amu) measure the mass of atoms and subatomic particles. It's a standard unit that allows scientists to compare the mass of different atoms. The atomic mass unit is defined as one twelfth the mass of a carbon-12 atom, which is approximately \(1.66 \times 10^{-24}\) grams.

Using atomic mass units simplifies the expressions of atomic and molecular masses since these quantities are incredibly small. For instance, the average atom of chromium has an atomic mass around 52 amu, which means that it is approximately 52 times as massive as one twelfth the mass of a carbon-12 atom. Understanding atomic mass units is paramount when students perform calculations involving molecular weights and when interpreting the molecular formulas of substances.