Question

WEB See the definition of isobars in Question 15. Consider Na-21 and write the nuclear symbol for (a) an isotope of Na-21 that has one more neutron than \(\mathrm{Na}-21\). (b) an isobar of Na-21 with atomic number 10 . (c) a nucleus with 11 protons and 12 neutrons. Is this nucleus an isotope of \(\mathrm{Na}-21\) ?

Short answer

Are the last two isotopes of Na-21? Answer: The nuclear symbols are: 1. Isotope of Na-21 with one more neutron: \(^{22}\mathrm{Na}-11\) 2. Isobar of Na-21 with atomic number 10: \(^{21}\mathrm{Ne}-10\) 3. Nucleus with 11 protons and 12 neutrons: \(^{23}\mathrm{Na}-11\) The last two are not both isotopes of Na-21. The nucleus with 11 protons and 12 neutrons (\(^{23}\mathrm{Na}-11\)) is an isotope of Na-21, while the isobar (\(^{21}\mathrm{Ne}-10\)) is not, as it has a different atomic number.

Step-by-step solution

Atomic Number (Z) and Mass Number (A)

An atom is represented by its element symbol (X), atomic number (Z), and mass number (A). The atomic number represents the number of protons (p) in the nucleus, while the mass number represents the total number of protons and neutrons (n) in the nucleus. The nuclear symbol is written as follows: \(^{A}\mathrm{X}-Z\)

Isotope of Na-21 with one more neutron

To derive the isotope of Na-21 with one more neutron, we can simply add one more neutron to Na-21's mass number, resulting in a new mass number, while keeping the same atomic number. Na-21 has an atomic number of 11 (Na) and a mass number of 21. New mass number = 21 + 1 = 22 So the isotope of Na-21 with one more neutron is: \(^{22}\mathrm{Na}-11\)

Isobar of Na-21 with atomic number 10

An isobar is an atom with the same mass number but a different atomic number. In this case, we are looking for an isobar of Na-21 with an atomic number of 10. Mass number = 21 (same as Na-21) Atomic number = 10 The element with an atomic number of 10 is neon (Ne). So the isobar of Na-21 is: \(^{21}\mathrm{Ne}-10\)

Nucleus with 11 protons and 12 neutrons

For this part, we need to find the nuclear symbol for a nucleus with 11 protons and 12 neutrons. The element with 11 protons is sodium (Na). Mass number = number of protons + number of neutrons = 11 + 12 = 23 So the nuclear symbol of this nucleus is: \(^{23}\mathrm{Na}-11\) As for whether this nucleus is an isotope of Na-21, the answer is yes. Na-21 and \(^{23}\mathrm{Na}-11\) both have the same atomic number (protons), but different mass numbers (total protons and neutrons), making them isotopes of each other.

Key concepts

Atomic Number

Understanding the atomic number is essential when discussing isotopes and isobars. The atomic number, often represented by the symbol 'Z', refers to the number of protons found in the nucleus of an atom. It is a unique identifier that determines the type of element. For instance, every atom with 11 protons is recognized as sodium (Na), regardless of how many neutrons it has. The atomic number not only defines the element but also its position in the periodic table, as elements are ordered by their atomic numbers.

Learning how to use the atomic number can help students differentiate between various forms of an element. For example, sodium (Na) has an atomic number of 11, which means every sodium atom will have 11 protons. Changes in neutron count create isotopes but do not affect the atomic number. To understand isotopes, such as the one described in the exercise, you'll primarily focus on the neutron count, while the atomic number remains unchanged.

Mass Number

The mass number, symbolized by 'A', represents the total number of protons and neutrons in an atom's nucleus. It is crucial when distinguishing between different isotopes of the same element. The mass number gives us information about the weight of an atom, since protons and neutrons make up most of an atom's mass. Atoms of an element with different mass numbers are isotopes of that element. For example, in the exercise, Na-21 has a mass number of 21 (11 protons and 10 neutrons), while its isotope with 12 neutrons will have a mass number of 22, denoted as ^{22}Na-11.

Understanding mass numbers is vital for identifying isobars as well, which are atoms with the same mass number but different atomic numbers. This concept is clearly illustrated in the solution, where Na-21 and ^{21}Ne-10 have the same mass number (21) but differ in their atomic numbers (11 for sodium and 10 for neon), making them isobars.

Nuclear Symbol

The nuclear symbol is a succinct way of representing an atom's key nuclear properties. It includes the element's symbol, mass number, and atomic number, usually written in the format ^{A}X-Z. This notation provides a visual snapshot of the atom, allowing you to quickly identify its element, how many protons it has, and the sum of protons and neutrons in the nucleus.

For instance, the nuclear symbol ^{22}Na-11 signifies that the sodium isotope has 11 protons (atomic number Z) and a mass number (A) of 22. In the exercise, learning to write and interpret the nuclear symbol is integral for determining the relationship between different isotopes and isobars. The nuclear symbol not only conveys critical information about an atom's structure but also facilitates the comparison between isotopes, such as ^{21}Na-11 and ^{23}Na-11, emphasizing the change in neutron count while the atomic number remains constant.