Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 40: Problem 15

Why are atomic nuclei more or less limited in size and neutron-proton ratios? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles?

Short Answer

Expert verified
Answer: The stability of atomic nuclei is governed by the balance of forces acting within the nucleus, specifically the short-range strong nuclear force and the long-range electrostatic repulsion force between protons. Atomic nuclei are limited in size and neutron-proton ratios due to the necessity of maintaining a balance between these forces. Having too many neutrons or very large nuclei with insufficient strong nuclear force would lead to unstable nuclei that undergo radioactive decay.

Step by step solution

01

Understanding Nucleus Stability

Stability of atomic nuclei is determined by the balance between two forces acting within the nucleus: the strong nuclear force, which holds the protons and neutrons together, and the electrostatic repulsion force between the protons due to their positive charge. The strong nuclear force is a short-range force, effective only over distances of about 1-2 femtometers (fm). In contrast, the electrostatic force is a long-range force, acting over much larger distances.
02

Neutron-Proton Ratios

A stable nucleus needs an appropriate neutron-proton ratio. Neutrons help to stabilize the nucleus by increasing the overall attractive strong nuclear force, without adding to the repulsive electrostatic force between protons. If the number of neutrons is too low or too high relative to the number of protons, the nucleus may become unstable and undergo radioactive decay. Having 10 times more neutrons than protons would lead to a very large neutron-proton imbalance. In such nuclei, the strong nuclear force would decrease significantly, and the repulsive electrostatic force between protons would dominate. This would lead to the nucleus becoming unstable and undergoing radioactive decay.
03

Nuclei Size Limitations

If we imagine an atomic nucleus with the size of a marble, it means the protons within the nucleus would be separated by a much larger distance than the typical strong nuclear force's effective range (1-2 femtometers). In such a nucleus, the repulsive electrostatic force between the protons would not be efficiently counteracted by the strong nuclear force, leading to an unstable nucleus. Another point to consider is that, in very large nuclei, the number of neutrons required to stabilize the nucleus would be enormous, resulting in extremely high neutron-proton ratios. Such a nucleus would be highly unstable and prone to undergoing radioactive decay.
04

Conclusion

The stability of atomic nuclei is governed by the balance of forces acting within the nucleus. Atomic nuclei are limited in size and neutron-proton ratios due to the short-range nature of the strong nuclear force and the necessity of maintaining a balance between this force and the electrostatic repulsion force between protons. Having too many neutrons or very large nuclei with insufficient strong nuclear force would lead to unstable nuclei that undergo radioactive decay.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a) What is the energy released in the fusion reaction \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+Q ?\) b) The oceans have a total mass of water of \(1.50 \cdot 10^{16} \mathrm{~kg}\), and \(0.0300 \%\) of this quantity is deuterium, \({ }_{1}^{2} \mathrm{H} .\) If all the deuterium in the oceans were fused by controlled fusion into \({ }_{2}^{4} \mathrm{He},\) how many joules of energy would be released? c) World power consumption is about \(1.00 \cdot 10^{13} \mathrm{~W}\). If consumption were to stay constant and all problems arising from ocean water consumption (including those of political, meteorological, and ecological nature) could be avoided, how many years would the energy calculated in part (b) last?

A drug containing \({ }_{43}^{99} \mathrm{Tc}\left(t_{1 / 2}=6.05 \mathrm{~h}\right)\) with an activity of \(1.50 \mu \mathrm{Ci}\) is to be injected into a patient at \(9.30 \mathrm{a} . \mathrm{m} .\) You are to prepare the sample \(2.50 \mathrm{~h}\) before the injection (at 7: 00 a.m.). What activity should the drug have at the preparation time (7:00 a.m.)?

\(^{8} \mathrm{Li}\) is an isotope that has a lifetime of less than one second. Its mass is \(8.022485 \mathrm{u} .\) Calculate its binding energy in \(\mathrm{MeV}\).

\(^{214} \mathrm{Pb}\) has a half-life of \(26.8 \mathrm{~min}\). How many minutes must elapse for \(90.0 \%\) of a given sample of \({ }^{214} \mathrm{~Pb}\) atoms to decay?

A certain radioactive isotope decays to one-eighth its original amount in \(5.00 \mathrm{~h} .\) How long would it take for \(10.0 \%\) of it to decay?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Solid State Physics

Read Explanation

Classical Mechanics

Read Explanation

Scientific Method Physics

Read Explanation

Energy Physics

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free