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Chapter 29: Problem 36

Only two isotopes of \(\mathrm{Sb}\) (antimony, \(Z=51\) ) are stable. Pick the two most likely stable isotopes from the follow- (b) \({ }^{121} \mathrm{Sb}\) ing list and explain your rationale: (a) \({ }^{120} \mathrm{Sb}\), (c) \(^{122} \mathrm{Sb} ;\) (d) \({ }^{123} \mathrm{Sb} ;\) (e) \({ }^{124} \mathrm{Sb}\)

Short Answer

Expert verified
The two most likely stable isotopes of \\mathrm{Sb}\\ are \\({ }^{121} \\mathrm{Sb}\\) and \\({ }^{123} \\mathrm{Sb}\\).

Step by step solution

01

Understanding Stability of Isotopes

Stable isotopes have a suitable balance between the number of protons and neutrons, allowing the nucleus to exist without undergoing radioactive decay. Antimony's atomic number is 51, meaning it has 51 protons. The stability of an isotope often depends on how close the neutron-to-proton ratio is to the ideal ratio for stability. For Antimony, the stable isotopes generally range around a neutron-to-proton ratio of approximately 1.2.
02

Calculating Neutron-to-Proton Ratios

To find the neutron-to-proton ratio, subtract the atomic number from the mass number (e.g., for \({ }^{121} \mathrm{Sb}\), it has 121 - 51 = 70 neutrons). Thus, the neutron-to-proton ratio is \((70/51)\approx 1.37\). Calculate similarly for other isotopes. - \({ }^{120} \mathrm{Sb}\): \(120 - 51 = 69\), ratio \(69/51 \approx 1.35\).- \({ }^{122} \mathrm{Sb}\): \(122 - 51 = 71\), ratio \(71/51 \approx 1.39\).- \({ }^{123} \mathrm{Sb}\): \(123 - 51 = 72\), ratio \(72/51 \approx 1.41\).- \({ }^{124} \mathrm{Sb}\): \(124 - 51 = 73\), ratio \(73/51 \approx 1.43\).
03

Comparing with Known Stable Isotopes

Research and historical data show \({ }^{121} \mathrm{Sb}\) and \({ }^{123} \mathrm{Sb}\) are naturally occurring stable isotopes of Antimony, with neutron-to-proton ratios close to 1.37 and 1.41, respectively. Isotopes with extreme neutron-to-proton ratios compared to these are less likely to be stable, supporting the choice of \({ }^{121} \mathrm{Sb}\) and \({ }^{123} \mathrm{Sb}\) as the stable isotopes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Antimony
Antimony, symbolized as Sb, is a chemical element with an atomic number of 51. This number is important because it tells us that antimony has 51 protons in each of its atomic nuclei. Protons are positively charged particles, and their number defines the element.
Antimony is a versatile element used in a variety of applications, such as in alloys to improve hardness and in flame retardants. The study of antimony isotopes helps scientists understand the element's properties better.

Antimony's place in the periodic table means it has properties of metals and metalloids. This makes it an interesting element when discussing the stability of isotopes.
Stable isotopes
Stable isotopes are forms of an element whose nuclei do not undergo radioactive decay. This stability comes down to the right balance between neutrons and protons in the nucleus. For antimony, stable isotopes have a neutron-to-proton ratio that sustains this balance.
Two naturally occurring stable isotopes of antimony are
  • \(^{121}\)Sb
  • \(^{123}\)Sb
The neutron-to-proton ratio is essential here because having too many or too few neutrons compared to protons can cause instability.
In this case, the ratios maintaining stability for antimony are close to 1.37 and 1.41. Isotopes outside of this ratio range are often unstable and likely to undergo radioactive decay.
Neutron-to-proton ratio
The neutron-to-proton ratio plays a crucial role in the stability of an isotope. Neutrons and protons are both in the atomic nucleus, and their balance is key for nuclear stability.
For antimony, the stable isotopes have a neutron-to-proton ratio around 1.2, but it鈥檚 more accurately around 1.37 to 1.41 as per naturally stable isotopes.
Here's how you can find the neutron-to-proton ratio:
  • Subtract the atomic number (number of protons) from the mass number (neutrons plus protons) to find the number of neutrons.
  • Divide the number of neutrons by the number of protons.
If the resulting ratio is close to 1.2 (or 1.37 to 1.41 for antimony), the isotope is typically stable.
Radioactive decay
Radioactive decay refers to the process by which unstable isotopes lose energy by emitting radiation. This can happen when the neutron-to-proton ratio in the nucleus is not balanced.
For isotopes of antimony that do not fall into the stable range, they become radioactive. This means they break down over time, emitting radiation to achieve a more stable form.
There are several types of radioactive decay, including:
  • Alpha decay
  • Beta decay
  • Gamma decay
Each type involves a different particle or energy emission, which helps the isotope move toward stability. Understanding these processes is crucial in fields like nuclear physics and chemistry.

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Most popular questions from this chapter

In a diagnostic procedure, a patient in a hospital ingests \(80 \mathrm{mCi}\) of gold- \(198\left(t_{1 / 2}=2.7\right.\) days \() .\) What is the activity at the end of one month, assuming none of the gold is eliminated from the body by biological functions?

A lead-209 nucleus results from both alpha-beta sequential decays and beta- alpha sequential decays. What was the grandparent nucleus? Show this result for both decay routes by writing the nuclear equations for both sequential decay processes.

Write the nuclear equations expressing (a) the beta decay of \({ }^{60} \mathrm{Co}\) and \((\mathrm{b})\) the alpha decay of \({ }^{222} \mathrm{Rn}\)

\({ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\) are two isotopes of chlorine. What are the numbers of protons, neutrons, and electrons in each if (a) the atom is electrically neutral, (b) the ion has a -2 charge, and (c) the ion has a +1 charge?

The experimental expression for the (approximate) radius \((R)\) of a nucleus is \(R=R_{\mathrm{o}} A^{1 / 3},\) where \(R_{\mathrm{o}}=1.2 \times 10^{-15} \mathrm{~m}\) and \(A\) is the mass number of the nucleus. Assuming that nuclei are spherical (they are approximately so in many cases), (a) determine the average nucleon density in a nucleus in units of nucleons \(/ \mathrm{m}^{3}\) and (b) estimate the nuclear density in \(\mathrm{kg} / \mathrm{m}^{3}\). Are you surprised at the magnitude of your answer? (c) A neutron star is the last phase of evolution for some types of stars. Typically, a neutron star has a diameter of \(15 \mathrm{~km}\) and a mass twice that of our Sun. Determine the average density of a typical neutron star and compare it to your answer to part (b). What can you conclude about the structure of the neutron star and how it got its name?
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