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Chapter 21: Problem 7

State the general rules for predicting nuclear stability.

Short Answer

Expert verified
The general rules to predict nuclear stability involve recognizing 'magic numbers' of protons or neutrons, maintaining a proper neutron to proton ratio, having an even number of protons and neutrons, staying within the band of stability, and considering the concept of 'Islands of Stability' for superheavy elements.

Step by step solution

01

Rule 1: Magic Numbers

The nuclei are observed to be most stable when the number of protons or neutrons it has is equal to any of the 'magic numbers': 2, 8, 20, 28, 50, 82, or 126. These specific numbers of protons or neutrons have higher binding energies which contribute to a nucleus's stability.
02

Rule 2: Neutron to Proton Ratio

For lighter elements (atomic number less than or equal to 20), stable nuclei have a neutron to proton ratio close to 1:1. But for heavier elements (atomic number greater than 20), the neutron to proton ratio increases as atomic number increases. This is because neutrons help to cushion the repulsive forces between protons in the nucleus, which are greater for elements with larger atomic numbers.
03

Rule 3: Even-Even Nuclei

Nuclei with an even number of both protons and neutrons are observed to be more stable. This can be explained by the pairing effect, which states that particles (like protons and neutrons) tend to pair up, resulting in increased stability.
04

Rule 4: Band of Stability

The band of stability is a region on a graph of Neutrons (N) versus Protons (Z) where stable nuclei are found. Nuclei outside of the band are unstable and undergo radioactive decay until they reenter the band.
05

Rule 5: Islands of Stability

There is a theoretical concept known as the 'Island of Stability' which pertains to superheavy elements. It suggests that certain superheavy nuclei with specific 'magic numbers' of protons and neutrons may have longer half-lives as a result of increased nuclear stability.

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Most popular questions from this chapter

The radioactive isotope \({ }^{238} \mathrm{Pu},\) used in pacemakers, decays by emitting an alpha particle with a half-life of 86 yr. (a) Write an equation for the decay process. (b) The energy of the emitted alpha particle is \(9.0 \times 10^{-13} \mathrm{~J}\), which is the energy per decay. Assume that all the alpha particle energy is used to run the pacemaker, calculate the power output at \(t=0\) and \(t=10 \mathrm{yr}\). Initially \(1.0 \mathrm{mg}\) of \({ }^{238} \mathrm{Pu}\) was present in the pacemaker (Hint: After \(10 \mathrm{yr}\), the activity of the isotope decreases by 8.0 percent. Power is measured in watts or \(\mathrm{J} / \mathrm{s}\).).

Consider this redox reaction: $$ \begin{array}{r} \mathrm{IO}_{4}^{-}(a q)+2 \mathrm{I}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\ \mathrm{I}_{2}(s)+\mathrm{IO}_{3}^{-}(a q)+2 \mathrm{OH}^{-}(a q) \end{array} $$ When \(\mathrm{KIO}_{4}\) is added to a solution containing iodide ions labeled with radioactive iodine- \(128,\) all the radioactivity appears in \(\mathrm{I}_{2}\) and none in the \(\mathrm{IO}_{3}^{-}\) ion. What can you deduce about the mechanism for the redox process?

A radioactive substance undergoes decay as: $$ \begin{array}{cc} \text { Time (days) } & \text { Mass (g) } \\ \hline 0 & 500 \\ 1 & 389 \\ 2 & 303 \\ 3 & 236 \\ 4 & 184 \\ 5 & 143 \\ 6 & 112 \end{array} $$ Calculate the first-order decay constant and the halflife of the reaction.

Outline the principle for dating materials using radioactive isotopes.

What makes water particularly suitable for use as moderator in a nuclear reactor?
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