Question

36\. Of the following isotopes, which are isotopes of the same element? a. \({ }_{10}^{20} \mathrm{X}\) b. \({ }_{10}^{22} \mathrm{X}\) c. \({ }_{11}^{22} \mathrm{X}\) d. \({ }_{12}^{20} \mathrm{X}\) e. \({ }_{9}^{21} \mathrm{X}\)

Short answer

The isotopes which are of the same element are: a. \({ }_{10}^{20} \mathrm{X}\) and b. \({ }_{10}^{22} \mathrm{X}\), as they have the same atomic number (Z = 10).

Step-by-step solution

Identify the atomic number (Z) and the mass number (A) in each isotope

First, let's list out the isotopes given in the problem, and identify their atomic number (Z) and mass number (A). a. \({ }_{10}^{20} \mathrm{X}\): Z = 10; A = 20 b. \({ }_{10}^{22} \mathrm{X}\): Z = 10; A = 22 c. \({ }_{11}^{22} \mathrm{X}\): Z = 11; A = 22 d. \({ }_{12}^{20} \mathrm{X}\): Z = 12; A = 20 e. \({ }_{9}^{21} \mathrm{X}\): Z = 9; A = 21

Compare the atomic numbers (Z) of each isotope

Since isotopes of the same element have the same number of protons (the same atomic number, Z), we can compare the atomic numbers of each isotope given. a and b: Z = 10; both have the same atomic number c: Z = 11 d: Z = 12 e: Z = 9

Identify the isotopes of the same element

Now that we've compared the atomic numbers, we can identify which isotopes are isotopes of the same element. In this case, the isotopes with the same atomic number, Z, are: a. \({ }_{10}^{20} \mathrm{X}\) b. \({ }_{10}^{22} \mathrm{X}\) So the isotopes a and b are isotopes of the same element.

Key concepts

Atomic Number

Understanding the atomic number is fundamental in chemistry. The atomic number, denoted as Z, is essentially the identity card for an element. It corresponds to the number of protons found in the nucleus of an atom. Every element has a unique atomic number which defines its chemical properties.

For example, in the exercise, isotope (a) \( {}_{10}^{20} \mathrm{X} \) and isotope (b) \( {}_{10}^{22} \mathrm{X} \) both have an atomic number of 10. This means they both have 10 protons and are therefore isotopes of the same element. Changes in the atomic number signify a change in the element itself, which is why isotope (c) \( {}_{11}^{22} \mathrm{X} \) represents a different element due to having an atomic number of 11.

Mass Number

The mass number, represented as A, refers to the total number of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number isn't fixed for a given element; it can vary leading to different isotopes of the same element. Isotopes share the same atomic number but differ in their mass numbers due to the varying number of neutrons.

In the given exercise, despite (a) \( {}_{10}^{20} \mathrm{X} \) and (b) \( {}_{10}^{22} \mathrm{X} \) being isotopes of the same element (both have an atomic number Z of 10), their mass numbers differ; 20 and 22 respectively. This tells us that (b) has two more neutrons than (a), which results in a greater atomic mass.

Nuclear Chemistry

Nuclear chemistry is the subfield of chemistry dealing with radioactive substances and nuclear processes including but not limited to fission, fusion, and radioactive decay. It delves deep into the behavior and transformation of elements at the level of the nucleus. Isotopes themselves are essential considerations within nuclear chemistry because their differences in neutrons can affect their nuclear stability and how they might respond in nuclear reactions.

For instance, an application of nuclear chemistry is seen in the usage of isotopes with different mass numbers in radiometric dating techniques, where the decay rates of isotopes provide crucial information on the age of artifacts and fossils.

Chemical Education

Chemical education plays a pivotal role in ensuring students understand the complexities of chemistry in an accessible manner. While tackling concepts such as atomic number and mass number might seem challenging, the goal is to break down these topics into comprehensible segments that facilitate learning.

Tools such as step-by-step solutions help demystify how to differentiate isotopes of the same element or understand their relevance in nuclear chemistry. Incorporating practical examples and interactive exercises can significantly enhance the learning process by connecting theoretical concepts with real-world applications.