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Chapter 2: Problem 25

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?

Short Answer

Expert verified
For lighter, stable isotopes, the ratio of the mass number (A) to the atomic number (Z) is close to 1 (A/Z 鈮� 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 by step solution

01

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.
02

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 鈮� 1.
03

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.

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Most popular questions from this chapter

Indium oxide contains \(4.784 \mathrm{~g}\) of indium for every \(1.000 \mathrm{~g}\) of oxygen. In 1869 , when Mendeleev first presented his version of the periodic table, he proposed the formula \(\mathrm{In}_{2} \mathrm{O}_{3}\) for indium oxide. Before that time it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of \(16.00\).

From the information in this chapter on the mass of the proton, the mass of the electron, and the sizes of the nucleus and the atom, calculate the densities of a hydrogen nucleus and a hydrogen atom.

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