Problem 23 - Chemistry An Atoms First Approach

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 approximately 2, meaning \(\frac{A}{Z} \approx 2\). As stable isotopes become heavier, the ratio \(\frac{A}{Z}\) increases due to the need for more neutrons to maintain stability in the nucleus against the stronger electrostatic repulsion caused by a larger number of protons.

Step 1: 1. Determining the ratio for lighter, stable isotopes

For lighter, stable isotopes, the ratio of the mass number (A) to the atomic number (Z) is approximately 2. This means that the mass number (number of protons and neutrons) is twice the atomic number (number of protons): \[ \frac{A}{Z} \approx 2 \]

Step 2: 2. Understanding the trend with heavier isotopes

As stable isotopes become heavier, the ratio \(\frac{A}{Z}\) increases. This is because adding more neutrons is necessary to increase the stability of the nucleus for elements with a higher atomic number (more protons). The larger number of protons leads to a stronger electrostatic repulsion within the nucleus, so adding more neutrons with their strong nuclear force helps offset this repulsion and maintain stability.

Step 3: 3. Conclusion

The ratio of the mass number to the atomic number for lighter, stable isotopes is approximately 2. As the isotopes become heavier, the value of this ratio increases due to the need for an increased number of neutrons for stability.