Question

Naturally occurring magnesium consists primarily of three isotopes, of mass numbers 24,25 , and 26 . How many protons does each of these nuclides contain? How many neutrons does each of these nuclides contain? Write nuclear symbols for each of these isotopes.

Short answer

All isotopes of magnesium have 12 protons. Mg-24 has 12 neutrons, Mg-25 has 13 neutrons, and Mg-26 has 14 neutrons. The nuclear symbols for these isotopes are \(\mathrm{^{24}Mg}\), \(\mathrm{^{25}Mg}\), and \(\mathrm{^{26}Mg}\), respectively.

Step-by-step solution

Find the atomic number of Magnesium

The atomic number of magnesium (Mg) can be found in the periodic table. The atomic number of magnesium is 12. This means that all isotopes of magnesium have 12 protons.

Find the number of neutrons for each isotope

Since we know that the atomic number of magnesium is 12, we can use the mass number formula to find the number of neutrons in each isotope. The mass number (A) is the sum of protons (Z) and neutrons (N): A = Z + N. - For Mg-24: \( 24 = 12 + N \Rightarrow N = 24-12 = 12\) - For Mg-25: \( 25 = 12 + N \Rightarrow N = 25-12 = 13\) - For Mg-26: \( 26 = 12 + N \Rightarrow N = 26-12 = 14\)

Write the nuclear symbols for each isotope

Now that we have the number of protons and neutrons for each isotope, we can write the nuclear symbols as follows: 1. Mg-24: The nuclear symbol for this isotope is \(\mathrm{^{24}Mg}\), indicating that it has 12 protons (from the atomic number) and 12 neutrons (as calculated above). 2. Mg-25: The nuclear symbol for this isotope is \(\mathrm{^{25}Mg}\), indicating that it has 12 protons and 13 neutrons. 3. Mg-26: The nuclear symbol for this isotope is \(\mathrm{^{26}Mg}\), indicating that it has 12 protons and 14 neutrons. In summary: - All isotopes of magnesium contain 12 protons. - Mg-24 has 12 neutrons, Mg-25 has 13 neutrons, and Mg-26 has 14 neutrons. - The nuclear symbols for these isotopes are \(\mathrm{^{24}Mg}\), \(\mathrm{^{25}Mg}\), and \(\mathrm{^{26}Mg}\), respectively.

Key concepts

Atomic Number

The atomic number is a fundamental characteristic of an element and is essential for understanding the basics of chemistry. It is denoted by the symbol 'Z' and refers to the number of protons found in the nucleus of an atom. Protons carry a positive charge, and because atoms are electrically neutral, the atomic number also indicates the number of electrons in an uncharged atom.

For magnesium, as with any element, the atomic number remains constant across all its isotopes. It is this property that defines the element: all atoms with an atomic number of 12 are magnesium atoms, regardless of the number of neutrons or the isotope. Thus, regardless of whether we are examining magnesium-24, magnesium-25, or magnesium-26, each will contain 12 protons in its nucleus.

Knowing the atomic number is crucial when writing nuclear symbols for isotopes or identifying an element in a compound. It is also used to organize elements in the periodic table, where elements are listed in increasing order of atomic number.

Neutron Number

While the atomic number (number of protons) defines an element, the neutron number contributes to defining the different isotopes of that element. The neutron number, represented by the symbol 'N', is the count of neutrons in the nucleus of an atom. Neutrons do not carry electric charge and thus do not affect the chemical properties of an element in the same way as protons or electrons do. However, they play a critical role in the stability and atomic mass of the atom.

To find the neutron number, we use the mass number 'A', which is the sum of protons (Z) and neutrons (N): \[ A = Z + N \.\] By knowing the mass number and the atomic number, we can calculate the number of neutrons as \[ N = A - Z \.\] For the isotopes of magnesium given in the exercise, we can use this formula to determine that Mg-24 has 12 neutrons, Mg-25 has 13 neutrons, and Mg-26 has 14 neutrons.

Different neutron numbers lead to the different isotopes of an element. These isotopes can vary in terms of nuclear stability and physical properties, which can be crucial in areas such as medical imaging, nuclear energy, and scientific research.

Nuclear Symbols

Nuclear symbols provide a shorthand way of representing isotopes, incorporating both the element and information about its protons and neutrons. A nuclear symbol is generally written as \[ \_^{A}\_X\Z \.\] where 'A' is the mass number (total number of protons and neutrons), 'X' is the chemical symbol of the element, and 'Z' is the atomic number (number of protons).

For example, using this notation for magnesium's isotopes, we have \[ \_^{24}\_Mg\12 \.\] for Mg-24, \[ \_^{25}\_Mg\12 \.\] for Mg-25, and \[ \_^{26}\_Mg\12 \.\] for Mg-26. These symbols convey at a glance that all three are magnesium isotopes (with 12 protons), but they differ in their neutron count and thus in their mass number. This nuclear notation is extensively used in chemistry and physics to quickly convey information about the composition of an atom without the need for lengthy explanations.

Understanding the proper use of nuclear symbols allows students and scientists alike to communicate complex information about isotopic composition succinctly. When analyzing chemical reactions or discussing elements, it is vital to recognize and be able to interpret these nuclear symbols accurately.