Problem 25 - Chemistry

Question

For lighter, stable isotopes, the ratio of the mass number to the atomic number is close to a certain value. What is the value? What happens to the value of the mass number to atomic number ratio as stable isotopes become heavier?

Step-by-Step Solution

Answer

For lighter, stable isotopes, the ratio of the mass number (A) to the atomic number (Z) is close to 1 (A/Z ≈ 1). This indicates that the number of protons and neutrons in the nucleus is almost equal. As stable isotopes become heavier, the repulsion between protons increases, requiring more neutrons to stabilize the nucleus. Consequently, the A/Z ratio increases (A/Z > 1) for heavier, stable isotopes as the number of neutrons becomes greater than the number of protons.

Step 1: Introduction to Isotopes

Isotopes are atoms of the same element (having the same number of protons) but having different numbers of neutrons. This results in different mass numbers (sum of protons and neutrons) for the isotopes of the same element. The mass number is represented by A, and the atomic number is represented by Z.

Step 2: Mass to Atomic Number Ratio for Lighter Isotopes

For lighter, stable isotopes (such as Hydrogen, Helium, Lithium, etc.) the ratio between the mass number (A) and the atomic number (Z) is close to 1. This means that for lighter elements, the number of protons and neutrons in the nucleus is almost equal, making them stable. So, for lighter, stable isotopes, the value of A/Z ≈ 1.

Step 3: Change in Mass to Atomic Number Ratio for Heavier Isotopes

As the isotopes become heavier, the repulsion between protons increases, which in turn requires more neutrons to stabilize the nucleus. Hence, the number of neutrons (N) starts becoming greater than the number of protons (Z) as the isotopes get heavier. Consequently, the mass number (A = Z + N) becomes greater than the atomic number (Z), and the A/Z ratio increases, i.e., A/Z > 1 for heavier, stable isotopes. In conclusion, for lighter, stable isotopes, the A/Z ratio is close to 1, whereas this ratio increases as isotopes become heavier due to an increased number of neutrons needed for stability.