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Chapter 10: Problem 5

To obtain the most precise value of the binding energy per nucleon, it is important to take into account forces between nucleons at the surface of the nucleus. Will surface effects increase or decrease estimates of BEN?

Short Answer

Expert verified
Considering surface effects in the calculation of binding energy per nucleon (BEN) provides a more accurate estimate, as it accounts for both the stronger interactions in the bulk of the nucleus and the weaker interactions at the surface. Surface nucleons have less energy than bulk nucleons, so the inclusion of surface effects will result in a decreased BEN estimate.

Step by step solution

01

Understanding BEN and bulk vs. surface nucleons

BEN is the energy required to disassemble a nucleus into its constituent nucleons. A higher BEN indicates a more stable nucleus. In a nucleus, nucleons are packed together and interact with each other through the strong nuclear force. The nucleons in the bulk of the nucleus interact with multiple neighboring nucleons, while those at the surface have fewer neighbors to interact with.
02

Comparing interaction energies for bulk and surface nucleons

The nucleons in the bulk of the nucleus have stronger interactions due to the attractive forces between them and multiple neighboring nucleons. In contrast, nucleons at the surface experience weaker interactions, as they do not have as many neighboring nucleons.
03

Understanding the effect of surface nucleons on BEN estimates

When estimating the BEN, if we do not take into account the weaker forces experienced by surface nucleons, we would assume that all nucleons in the nucleus experience the same strong interactions. This would lead to an overestimation of the energy required to disassemble the nucleus.
04

Concluding the effect of surface effects on BEN estimates

Taking surface effects into account provides a more accurate BEN estimate, as it considers both the stronger interactions in the bulk of the nucleus and the weaker interactions at the surface. By doing so, the overall estimate of the binding energy per nucleon is reduced because surface nucleons have less energy than bulk nucleons. Therefore, the consideration of surface effects will decrease estimates of BEN.

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Most popular questions from this chapter

(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture. (b) If this process takes place continuously over a period of a year, what is the average power output?

Show that the total energy released in the proton-proton chain is \(26.7 \mathrm{MeV},\) considering the overall effect in \(^{1} \mathrm{H}+^{1} \mathrm{H} \rightarrow^{2} \mathrm{H}+e^{+}+v_{\mathrm{e}},^{1} \mathrm{H}+^{2} \mathrm{H} \rightarrow^{3} \mathrm{He}+\gamma,\) and \(^{3} \mathrm{He}+^{3} \mathrm{He} \rightarrow^{4} \mathrm{He}+^{1} \mathrm{H}+^{1} \mathrm{H} .\) Be sure to include the annihilation energy.

Explain why a bound system should have less mass than its components. Why is this not observed traditionally, say, for a building made of bricks?

For the reaction, \(n+^{3} \mathrm{He} \rightarrow^{4} \mathrm{He}+\gamma,\) find the amount of energy transfers to \(^{4} \mathrm{He}\) and \(\gamma\) (on the right side of the equation). Assume the reactants are initially at rest. (Hint: Use conservation of momentum principle.)

If a 1.50 -cm-thick piece of lead can absorb \(90.0 \%\) of the rays from a radioactive source, how many centimeters of lead are needed to absorb all but \(0.100 \%\) of the rays?
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