Problem 24 - Chemistry The Science in Context

Question

In each of the following pairs of isotopes, select the isotope that has more protons and the isotope that has more neutrons. Also indicate which pairs of isotopes have the same number of neutrons or protons. (a) \(^{63} \mathrm{Cu}\) and \(^{65} \mathrm{Cu}\) (b) \(^{71}\) Ga and \(^{71} \mathrm{Ge} ;\) (c) \(^{39} \mathrm{K}\) and \(^{40} \mathrm{Ar}\)

Step-by-Step Solution

Answer

A) \(^{63} \mathrm{Cu}\) and \(^{65} \mathrm{Cu}\) B) \(^{71} \mathrm{Ga}\) and \(^{71} \mathrm{Ge}\) C) \(^{39} \mathrm{K}\) and \(^{40} \mathrm{Ar}\) Answer: A) Both isotopes have the same number of protons (29). \(^{65} \mathrm{Cu}\) has more neutrons (36) than \(^{63} \mathrm{Cu}\) (34). B) \(^{71} \mathrm{Ge}\) has more protons (32), and \(^{71} \mathrm{Ga}\) has more neutrons (40). C) \(^{39} \mathrm{K}\) has more protons (19), and \(^{40} \mathrm{Ar}\) has more neutrons (22).

Step 1: Comparison A: \(^{63} \mathrm{Cu}\) and \(^{65} \mathrm{Cu}\)#

Both isotopes are copper (Cu), which has the atomic number (number of protons) Z = 29. So, both isotopes have the same number of protons. For the number of neutrons, we calculate for each isotope: - \(^{63} \mathrm{Cu}\): N = 63 - 29 = 34 - \(^{65} \mathrm{Cu}\): N = 65 - 29 = 36 Thus, \(^{65} \mathrm{Cu}\) has more neutrons than \(^{63} \mathrm{Cu}\).

Step 2: Comparison B: \(^{71} \mathrm{Ga}\) and \(^{71} \mathrm{Ge}\)#

For gallium (Ga), the atomic number is Z = 31. For germanium (Ge), the atomic number is Z = 32. As a result, \(^{71} \mathrm{Ge}\) has more protons. For the number of neutrons, we calculate for each isotope: - \(^{71} \mathrm{Ga}\): N = 71 - 31 = 40 - \(^{71} \mathrm{Ge}\): N = 71 - 32 = 39 Thus, \(^{71} \mathrm{Ga}\) has more neutrons than \(^{71} \mathrm{Ge}\).

Step 3: Comparison C: \(^{39} \mathrm{K}\) and \(^{40} \mathrm{Ar}\)#

For potassium (K), the atomic number is Z = 19. For argon (Ar), the atomic number is Z = 18. As a result, \(^{39} \mathrm{K}\) has more protons. For the number of neutrons, we calculate for each isotope: - \(^{39} \mathrm{K}\): N = 39 - 19 = 20 - \(^{40} \mathrm{Ar}\): N = 40 - 18 = 22 Thus, \(^{40} \mathrm{Ar}\) has more neutrons than \(^{39} \mathrm{K}\).

Key Concepts

Atomic Number

The atomic number, often denoted by the symbol Z, is a fundamental characteristic of an element that defines its identity. It represents the number of protons found in the nucleus of an atom. Since each element has a unique number of protons, the atomic number serves as its fingerprint on the periodic table.

For example, in the given exercise, copper (Cu) has an atomic number of 29, meaning that all copper atoms contain 29 protons in their nucleus, regardless of the isotope. The atomic number is crucial for understanding the concept of isotopes, as it remains constant for all isotopes of the same element, distinguishing them from other elements.

Neutrons in Isotopes

Isotopes of an element have the same atomic number, which means they have the same number of protons, but they differ in the number of neutrons. The total number of neutrons in an isotope can be determined by subtracting the atomic number (protons) from the atomic mass number (symbol A), which is the sum of protons and neutrons. This difference is denoted as N, the neutron number.

In our exercise, calculation such as N = 65 - 29 = 36 for ⁶⁵Cu shows that it has 36 neutrons. Comparing different isotopes reveals whether one has more neutrons than another. For instance, ⁶⁵Cu has more neutrons than ⁶³Cu, as illustrated by the calculations in the provided solution.

Protons in Isotopes

While the number of neutrons can vary among isotopes of the same element, the number of protons, represented by the atomic number, remains consistent. This uniformity means that the chemical properties of isotopes will be very similar, as they are determined largely by the electron configuration — which is dictated by the number of protons.

Even when comparing isotopes across different elements, as in the comparison between ⁷¹Ga and ⁷¹Ge, it is the atomic number that distinguishes one element from another. In our example, germanium has more protons than gallium, as their atomic numbers are 32 and 31 respectively. Thus, the isotope ⁷¹Ge has more protons than ⁷¹Ga, but ⁷¹Ga has more neutrons, reflecting the inverse relationship between the number of neutrons and protons within isotopes having the same atomic mass number.