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Chapter 30: Problem 65

Which type of radioactive decay produces \({ }^{131} \mathrm{I}\) from \({ }^{131} \mathrm{Te} ?\) A. Alpha decay B. Beta-minus decay C. Beta-plus decay D. Gamma decay

Short Answer

Expert verified
Beta-minus decay (Option B) produces \(^{131}\text{I}\) from \(^{131}\text{Te}\).

Step by step solution

01

Understand the given isotopes

We are given two isotopes: \(^{131}\text{Te}\) and \(^{131}\text{I}\). We need to determine how \(^{131}\text{Te}\) changes into \(^{131}\text{I}\). Both isotopes have the same mass number 131.
02

Determine the atomic numbers

The atomic number of \(^{131}\text{Te}\) (Tellurium) is 52, while the atomic number of \(^{131}\text{I}\) (Iodine) is 53.
03

Analyze the change required

To change from \(^{131}\text{Te}\) to \(^{131}\text{I}\), tellurium must increase its atomic number by one unit without changing its mass number.
04

Choose the correct type of decay

Beta-minus decay involves the transformation of a neutron into a proton, which increases the atomic number by one while maintaining the same mass number. This process perfectly aligns with the transformation of \(^{131}\text{Te}\) (atomic number 52) to \(^{131}\text{I}\) (atomic number 53).
05

Rule out other options

Alpha decay would decrease both the atomic number and mass number by 4 and 2, respectively. Beta-plus decay would decrease the atomic number by one. Gamma decay does not change atomic number or mass. Hence, these are not suitable.
06

Conclude with the correct answer

Thus, the transformation of \(^{131}\text{Te}\) into \(^{131}\text{I}\) is due to beta-minus decay.

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Key Concepts

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

Isotopes
Isotopes are fascinating variations of chemical elements that share the same number of protons but differ in the number of neutrons. This difference gives isotopes distinct properties even though they are of the same element. Imagine isotopes as siblings in a family. While they share the same last name (or elemental identity), each brings its unique traits to the family portrait.
For example, the isotopes in our original problem,
  • Tellurium-131 (\( {}^{131} ext{Te} \))
  • Iodine-131 (\( {}^{131} ext{I} \))
They have the same mass number, but they belong to different elements because of their differing atomic numbers. Isotopes play an important role in areas such as
  • nuclear medicine,
  • energy production,
  • and dating of archaeological finds.
Beta-minus decay
Beta-minus decay is a specific type of radioactive decay that changes the identity of a nucleus while keeping its mass number the same. During this process, a neutron in the nucleus is transformed into a proton. This transformation is accompanied by the emission of a beta particle, which is essentially a high-energy electron.
What's interesting is how a neutron subtly rebalances itself to become a proton.
  • The atomic number of the nucleus increases by one.
  • The mass number, intriguingly, remains unchanged.
In our example, \( {}^{131} ext{Te} \) undergoes beta-minus decay to become \( {}^{131} ext{I} \) as:
  • A neutron becomes a proton.
  • And an electron (beta particle) is released.
Atomic number transformation
Atomic numbers are fundamental to understanding how elements transform during nuclear reactions. Each element on the periodic table has its unique atomic number, representing the number of protons in its nucleus.
During atomic transformations, like in our beta-minus decay example, \( {}^{131} ext{Te} \) to \( {}^{131} ext{I} \), attention is focused on these changes in proton numbers.
  • For \( {}^{131} ext{Te} \), the atomic number is 52.
  • When a neutron becomes a proton, the atomic number becomes 53, changing the element to iodine.
This increase in atomic number signifies a new element has formed, even though the isotopes still share the same mass number.
Nuclear physics
Nuclear physics delves into the exciting world of atomic nuclei and their components. Unlike classical physics, which focuses on actions we can see and touch, nuclear physics explores things at an atomic scale.
The transformations and reactions explained by nuclear physics have broad implications, ranging from generating electricity to medical applications. Understanding processes like beta-minus decay or isotope behavior not only tells us how elements change but also helps harness these changes for technological uses.
  • Nuclear power plants use these principles for energy.
  • Medical imaging techniques rely on these transformations to accurately diagnose diseases.
When we learn how nuclei respond under different conditions, we unlock a potential for sustainable energy and innovations in healthcare.
Mass number
The mass number of an atom refers to the total number of protons and neutrons in its nucleus. It provides a way to distinguish isotopes from each other, as isotopes of the same element share the same atomic number but have different numbers of neutrons.
In our example with \( {}^{131} ext{Te} \) and \( {}^{131} ext{I} \):
  • The mass number for both isotopes is 131.
  • This is calculated by adding the number of protons and neutrons together.
What's intriguing is the stability and properties that result from these differences and how they influence the radioactive decay processes. Understanding mass numbers helps clarify why certain substances are radioactive and how they might change over time or under certain conditions.

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Most popular questions from this chapter

At the beginning of Section \(30.6,\) a fission process is illustrated in which \({ }^{235} \mathrm{U}\) is struck by a neutron and undergoes fission to produce \({ }^{144} \mathrm{Ba},{ }^{89} \mathrm{Kr},\) and three neutrons. The measured masses of these isotopes are \(235.043930 \mathrm{u}\left({ }^{235} \mathrm{U}\right), 143.922953 \mathrm{u}\left({ }^{144} \mathrm{Ba}\right), 88.917630 \mathrm{u}\) \(\left({ }^{89} \mathrm{Kr}\right),\) and \(1.0086649 \mathrm{u}\) (neutron). (a) Calculate the energy (in \(\mathrm{MeV}\) ) released by each fission reaction. (b) Calculate the energy released per gram of \({ }^{235} \mathrm{U},\) in \(\mathrm{MeV} / \mathrm{g} .\)

Given that each particle contains only combinations of \(u, d, s,\) \(\bar{u}, \bar{d},\) and \(\bar{s},\) deduce the quark content of (a) a particle with charge \(+e,\) baryon number \(0,\) and strangeness \(+1 ;\) (b) a particle with charge \(+e,\) baryon number \(-1,\) and strangeness \(+1 ;\) (c) a particle with charge \(0,\) baryon number \(+1,\) and strangeness -2.

(a) Using the empirical formula for the radius of a nucleus, show that the volume of a nucleus is directly proportional to its nucleon number \(A\). (b) Give a reasonable argument concluding that the mass \(m\) of a nucleus of nucleon number \(A\) is approximately \(m=m_{\mathrm{p}} A,\) where \(m_{\mathrm{p}}\) is the mass of a proton. (c) Use the results of parts (a) and (b) to show that all nuclei should have about the same density. Then calculate this density in \(\mathrm{kg} / \mathrm{m}^{3}\), and compare it with the density of lead (which is \(\left.11.4 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and a neutron star (about \(10^{17} \mathrm{~kg} / \mathrm{m}^{3}\) ).

A photon with a wavelength of \(3.50 \times 10^{-13} \mathrm{~m}\) strikes a deuteron, splitting it into a proton and a neutron. (a) Calculate the kinetic energy released in this interaction. (b) Assuming the two particles share the energy equally, and taking their masses to be \(1.00 \mathrm{u},\) calculate their speeds after the photodisintegration.

(a) If a chest X-ray delivers \(0.25 \mathrm{mSv}\) to \(5.0 \mathrm{~kg}\) of tissue, how many total joules of energy does this tissue receive? (b) Natural radiation and cosmic rays deliver about \(0.10 \mathrm{mSv}\) per year at sea level. Assuming an \(\mathrm{RBE}\) of \(1,\) how many rem and rads is this dose, and how many joules of energy does a 75-kg person receive in a year? (c) How many chest X-rays like the one in part (a) would it take to deliver the same total amount of energy to a \(75-\mathrm{kg}\) person as she receives from natural radiation in a year at sea level, as described in part (b)?
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