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Chapter 21: Problem 12

Why is it preferable to use nuclear binding energy per nucleon for a comparison of the stabilities of different nuclei?

Short Answer

Expert verified
Nuclear binding energy per nucleon is a preferable measure for comparing the stability of different nuclei because it provides an average measure of how tightly each individual proton or neutron is bound within the nucleus. Larger nuclei naturally have larger total binding energies due to their size, but this doesn't necessarily mean they are more stable. The per nucleon measure allows for a more accurate stability comparison regardless of the size of the nuclei.

Step by step solution

01

Understanding Nuclear Binding Energy

Nuclear binding energy is the amount of energy required to disassemble a nucleus of an atom into its component protons and neutrons. It is a measure of the strength of the force that holds the nucleus together, and hence, a measure of the stability of the nucleus.
02

Understanding Per Nucleon Measurement

The term 'per nucleon' refers to the average binding energy per proton or neutron in the nucleus. It is calculated by dividing the total binding energy of a nucleus by the number of protons and neutrons it contains.
03

Correlation Between Nuclear Binding Energy Per Nucleon and Stability of Nuclei

In a comparison of the stabilities of different nuclei, using the total nuclear binding energy might be misleading because larger nuclei naturally tend to have larger binding energies due to their size. However, this does not necessarily mean that they are more stable. By considering the binding energy per nucleon, one can compare how tightly each individual nucleon is bound within the nucleus, which is a more accurate measure of nuclear stability. High binding energy per nucleon indicates a stable nucleus, while a low binding energy per nucleon suggests a less stable nucleus.

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Most popular questions from this chapter

Modern designs of atomic bombs contain, in addition to uranium or plutonium, small amounts of tritium and deuterium to boost the power of explosion. What is the role of tritium and deuterium in these bombs?

Describe, with appropriate equations, nuclear processes that lead to the formation of the noble gases He, Ne, Ar, Kr, Xe, and Rn. (Hint: Helium is formed from radioactive decay, neon is formed from the positron emission of \({ }^{22} \mathrm{Na}\), the formation of \(\mathrm{Ar}\), Xe, and \(\mathrm{Rn}\) are discussed in the chapter, and \(\mathrm{Kr}\) is produced from the fission of \(\left.{ }^{235} \mathrm{U} .\right)\)

Bismuth-214 is an \(\alpha\) -emitter with a half-life of 19.7 min. A 5.26 -mg sample of the isotope is placed in a sealed, evacuated flask of volume \(20.0 \mathrm{~mL}\) at \(40^{\circ} \mathrm{C}\). Assuming that all the \(\alpha\) particles generated are converted to helium gas and that the other decay product is nonradioactive, calculate the pressure (in \(\mathrm{mmHg}\) ) inside the flask after 78.8 min. Use 214 amu for the atomic mass of bismuth.

How does a Geiger counter work?

Write balanced nuclear equations for these reactions and identify \(\mathrm{X}:\) (a) \(\mathrm{X}(\mathrm{p}, \alpha){ }_{6}^{12} \mathrm{C},\) (b) \({ }_{13}^{27} \mathrm{Al}(\mathrm{d}, \alpha) \mathrm{X}\) (c) \({ }_{25}^{55} \mathrm{Mn}(\mathrm{n}, \gamma) \mathrm{X}\)
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