Question

What are the differences in the compositions of the following pairs of atomic nuclei? (a) \({ }_{83}^{210} \mathrm{Bi},{ }_{82}^{210} \mathrm{~Pb}\); (b) \({ }_{7}^{14} \mathrm{~N},{ }_{7}^{15} \mathrm{~N}\); (c) \({ }_{10}^{20} \mathrm{Ne},{ }_{18}^{40} \mathrm{Ar}\)

Short answer

In summary, the differences in the compositions of the given atomic nuclei pairs are as follows: (a) Bismuth has 1 more proton and 1 less neutron than Lead. (b) The second Nitrogen isotope has 1 more neutron than the first Nitrogen isotope, but the same number of protons. (c) Argon has 8 more protons and 12 more neutrons than Neon.

Step-by-step solution

Pair (a) \({ }_{83}^{210} \mathrm{Bi},{ }_{82}^{210} \mathrm{~Pb}\) #

To find the difference in the composition of these two atomic nuclei, we can subtract their respective proton and neutron numbers. The first element is Bismuth (Bi) with atomic number 83 and mass number 210, and the second element is Lead (Pb) with atomic number 82 and mass number 210. We can calculate the number of neutrons for both of them using the formula: Number of neutrons = Mass number - Atomic number For Bismuth, the number of neutrons = \(210 - 83 = 127\) For Lead, the number of neutrons = \(210 - 82 = 128\) So, the difference in the composition is 1 proton and 1 neutron. Bismuth has 1 more proton and 1 less neutron than Lead.

Pair (b) \({ }_{7}^{14} \mathrm{~N},{ }_{7}^{15} \mathrm{~N}\) #

Both isotopes in this pair are Nitrogen (N) with atomic number 7. The only difference is in the mass number, which is 14 in the first isotope and 15 in the second isotope. We can calculate the number of neutrons for both of them using the formula mentioned earlier: For the first Nitrogen isotope, the number of neutrons = \(14 - 7 = 7\) For the second Nitrogen isotope, the number of neutrons = \(15 - 7 = 8\) So, the difference in the composition is 0 protons and 1 neutron. The second Nitrogen isotope has 1 more neutron than the first Nitrogen isotope.

Pair (c) \({ }_{10}^{20} \mathrm{Ne},{ }_{18}^{40} \mathrm{Ar}\) #

The first atomic nucleus is Neon (Ne) with atomic number 10 and mass number 20, and the second one is Argon (Ar) with atomic number 18 and mass number 40. We can calculate the number of neutrons for both of them using the formula given earlier: For Neon, the number of neutrons = \(20 - 10 = 10\) For Argon, the number of neutrons = \(40 - 18 = 22\) So, the difference in the composition is 8 protons and 12 neutrons. Argon has 8 more protons and 12 more neutrons than Neon.

Key concepts

Isotopes and Nuclides

A foundational knowledge about atoms involves understanding nuclides and isotopes. Nuclides are species of atoms characterized by the constitution of their nuclei, specifically the number of protons and neutrons they contain. Each nuclide is identified by the atomic number (number of protons, denoted as Z) and the mass number (total number of protons and neutrons, denoted as A).

Isotopes, on the other hand, are variants of a particular chemical element that have the same number of protons (and hence the same atomic number) but differ in the number of neutrons, and consequently, in their mass number. This is notably displayed in pair (b) of our problem, \({ }_{7}^{14} \mathrm{~N},{ }_{7}^{15} \mathrm{~N}\), where the two nitrogen isotopes have the same atomic number but different mass numbers due to the difference in their neutron count.

Understanding isotopes is crucial because they can have slightly varied properties and can be used in a wide range of applications from dating archaeological artifacts to treating cancer.

Neutron Number Calculation

The neutron number is a critical property of an atomic nucleus and can be computed with a simple formula:
Number of neutrons = Mass number - Atomic number
For instance, with \({ }_{83}^{210} \mathrm{Bi}\) and \({ }_{82}^{210} \mathrm{~Pb}\), even though both have the same mass number, the number of neutrons in each nuclide can be calculated as 127 and 128, respectively. This calculation is fundamental to identifying isotopes and understanding the differences in their nuclear composition, as isotopes have different numbers of neutrons despite the same atomic number.

It’s worth mentioning that the neutron number is directly related to the stability of an isotope; isotopes with too many or too few neutrons compared to protons can be radioactive. Hence, calculating neutron numbers helps in classifying stable and radioactive isotopes.

Atomic Number and Mass Number

The atomic number (Z) and the mass number (A) are two important identifiers for elements. The atomic number represents the number of protons in the nucleus and, because it defines the chemical properties of the element, it is also the basis for the element's position in the Periodic Table. For example, the atomic numbers in pair (c), \({ }_{10}^{20} \mathrm{Ne},{ }_{18}^{40} \mathrm{Ar}\), tell us they are neon and argon, respectively.

The mass number is the sum of protons and neutrons in the nucleus. It is an approximation of the atomic mass, which is measured in atomic mass units. In our examples, the mass number gives insight into the overall size and mass of the nucleus, and when paired with a known atomic number, it allows us to calculate the neutron number as seen earlier.

Together, the atomic number and mass number provide a complete picture of the nucleus's composition, which is essential for understanding atomic structure and the subtle differences between different atoms and isotopes.