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Chapter 19: Problem 14

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 preferred for comparing the stabilities of different nuclei because it levels the playing field for different sizes of nuclei. The larger the binding energy per nucleon, the more stable the nucleus. It provides a more accurate comparison, unlike total binding energies which can give skewed results for isotopes and elements with different numbers of nucleons.

Step by step solution

01

Understand the concept of Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus of an atom into its constituent protons and neutrons. It is also the energy that is released when a nucleus is formed from its constituent protons and neutrons. However, a nucleus is composed of several nucleons (the term for either a proton or neutron), and each nucleon has a certain contribution to this total binding energy.
02

Define nuclear binding energy per nucleon

The nuclear binding energy per nucleon is defined as the binding energy divided by the number of nucleons. \[BindingEnergyPerNucleon = \frac{TotalBindingEnergy}{NumberOfNucleons}\] The unit of nuclear binding energy per nucleon is MeV/nucleon. The binding energy per nucleon provides a measurement of nuclear stability. Larger the value of binding energy per nucleon, more stable is the nucleus.
03

Obtain the utility of binding energy per nucleon in comparing nuclear stabilities

Because different isotopes and elements have different numbers of nucleons, comparing total binding energies can give skewed effects. That’s why, it's more accurate to compare nuclear binding energy per nucleon when we're comparing the stabilities of different atomic nuclei. When the binding energy per nucleon is high, it means the nucleus is tightly bound and therefore more stable. On the other hand, if the binding energy per nucleon is low, the nucleus is weakly bound and hence less stable. So, to effectively compare the stability of different nuclei, we consider nuclear binding energy per nucleon as it provides a level playing field.

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Most popular questions from this chapter

A 0.0100 -g sample of a radioactive isotope with a half-life of \(1.3 \times 10^{9} \mathrm{yr}\) decays at the rate of \(2.9 \times\) \(10^{4} \mathrm{dpm} .\) Calculate the molar mass of the isotope.

Explain the functions of a moderator and a control rod in a nuclear reactor.

The quantity of a radioactive material is often measured by its activity (measured in curies or millicuries) rather than by its mass. In a brain scan procedure, a \(70-\mathrm{kg}\) patient is injected with \(20.0 \mathrm{mCi}\) of \({ }^{99 \mathrm{~m}} \mathrm{Tc},\) which decays by emitting \(\gamma\) -ray photons with a half-life of \(6.0 \mathrm{~h}\). Given that the \(\mathrm{RBE}\) of these photons is 0.98 and only two-thirds of the photons are absorbed by the body, calculate the rem dose received by the patient. Assume all of the \({ }^{99 \mathrm{~m}} \mathrm{Tc}\) nuclei decay while in the body. The energy of a gamma photon is \(2.29 \times 10^{-14} \mathrm{~J}\).

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