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Chapter 18: Problem 13

A. What is the relationship among the number of protons, the number of neutrons, and the stability of the nucleus for small atoms? B. What is the relationship among number of protons, the number of neutrons, and the stability of the nucleus for large atoms?

Short Answer

Expert verified
The relationship among the number of protons, neutrons, and the stability of the nucleus for small atoms is that they are usually equal in number or have a near-equal ratio. While for larger atoms, to maintain stability, need more neutrons than protons to counteract the electrostatic repulsion among the many protons in the large nucleus. The stability of a nucleus, in both small and large atoms, relies on achieving a balance between the attractive strong nuclear force and the repulsive electrostatic force.

Step by step solution

01

Understanding Nuclear Stability

The stability of a nucleus is dependent on its atomic number. A stable nucleus has an equal number of protons and neutrons, which means it has a 1:1 neutron to proton ratio. The strong nuclear force that binds protons and neutrons together in the nucleus stabilizes the nucleus against the repulsive force between protons. Small atoms are more stable when they have an equal number of protons and neutrons (Z=N) or a near equal ratio.
02

Explaining Nuclear Stability in Small Atoms

In small atoms, the number of protons and neutrons is nearly equal due to the dominance of the strong nuclear force in maintaining stability against the electrostatic repulsion between protons within the small volume of the nucleus. This means the force is strong enough to keep the nucleus together.
03

Explaining Nuclear Stability in Large Atoms

For larger atoms, the strong nuclear force, which is short-range, cannot fully counteract the long-range electrostatic repulsion among the many protons in the large nucleus. Therefore, larger atoms require a greater number of neutrons to stabilize the nucleus. Here the neutron to proton ratio is greater than 1. So, the number of neutrons is higher than the number of protons to maintain a stable nucleus.

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Most popular questions from this chapter

Medium-mass nuclei have larger binding energies per nucleon than heavier nuclei do. What can you conclude from this fact?

Write the nuclear equation for the release of an alpha particle by \(_{70}^{157} \mathrm{Yb} .\)

Write the nuclear equation for the release of a beta particle by \(_{210}^{82} \mathrm{Pb} .\)

Why do animals contain the same ratio of carbon-14 to carbon-12 as plants do?

Calculating the Amount of Radioactive Material The graphing calculator can run a program that graphs the relationship between the amount of radioactive material and elapsed time. Given the half-life of the radioactive material and the initial amount of material in grams, you will graph the relationship between the amount of radioactive material and the elapsed time. Then, with the elapsed time, you will trace the graph to calculate the amount of radioactive material. Go to Appendix C. If you are using a TI-83 Plus, you can download the program RADIOACT and run the application as directed. If you are using another calculator, your teacher will provide you with key-strokes and data sets to use. After you have run the program, answer these questions. a. Determine the amount of neptunium-235 left after 2.0 years, given the half- life of neptunium-235 is 1.08 years and the initial amount was 8.00 g. b. Determine the amount of neptunium-235 left after 5.0 years, given the half- life of neptunium-235 is 1.08 years and the initial amount was 8.00 g. c. Determine the amount of uranium-232 left after 100 years, given the half- life of uranium-232 is 69 years and the initial amount was 10.0 g.
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