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What particle \((\alpha\) particle, electron, or positron) is emitted in the following radioactive decays? (a) \(_{14}^{27} \mathrm{Si} \rightarrow_{13}^{27} \mathrm{Al}\) (b) \(^{238} \mathrm{U} \rightarrow_{90}^{234} \mathrm{Th} ;\) (c) \(_{33}^{74} \mathrm{As} \rightarrow_{34}^{74} \mathrm{Se}\)

Short Answer

Expert verified
(a) Positron, (b) Alpha particle, (c) Electron

Step by step solution

01

Understand the Process

Radioactive decay is a process where an unstable atom loses energy by emitting radiation. The type of particle emitted determines the decay process: alpha decay emits an alpha particle, beta decay emits an electron or a positron.
02

Analyze (a) Silicon to Aluminum Decay

In the decay \(_{14}^{27} \mathrm{Si} \rightarrow_{13}^{27} \mathrm{Al}\),we see that the atomic number decreases by 1 while the mass number remains the same. This indicates the emission of a positron, which is characteristic of \(\beta^+\) (beta plus) decay.
03

Analyze (b) Uranium to Thorium Decay

In the decay \(^{238} \mathrm{U} \rightarrow_{90}^{234} \mathrm{Th}\),the atomic number decreases by 2 and the mass number decreases by 4, indicating the emission of an alpha particle (\(_{2}^{4}\mathrm{He}\)).
04

Analyze (c) Arsenic to Selenium Decay

In the decay \(_{33}^{74} \mathrm{As} \rightarrow_{34}^{74} \mathrm{Se}\),the atomic number increases by 1 whereas the mass number stays the same, signifying the emission of an electron (beta particle), characteristic of \(\beta^-\) decay.

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Key Concepts

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

Alpha Decay
Alpha decay is a fundamental concept in nuclear physics, where an unstable nucleus emits an alpha particle to become a more stable nucleus. An alpha particle is composed of two protons and two neutrons, identical to a helium nucleus \((_{2}^{4}\mathrm{He})\). This process results in a decrease in the atomic number by 2 and the mass number by 4.

For example, when uranium-238 undergoes alpha decay, it transforms into thorium-234. The equation is as follows: \[_{92}^{238}\mathrm{U} \rightarrow _{90}^{234}\mathrm{Th} + _{2}^{4}\mathrm{He} \]
  • The nucleus of uranium loses two protons and two neutrons.
  • This decreases the atomic number from 92 to 90.
  • The mass number decreases from 238 to 234.
Alpha decay generally occurs in heavy elements where the strong nuclear force struggles to hold a large nucleus together. Understanding alpha decay helps in studying radioactive materials and predicting how they will change over time.
Beta Decay
Beta decay is another type of radioactive decay involving the emission of a beta particle, which can either be an electron or a positron. It occurs in two forms, beta minus (\(\beta^-\)) decay and beta plus (\(\beta^+\)) decay.

In beta minus decay, a neutron within the nucleus is converted into a proton and an electron. The electron is ejected from the atom, leaving the nucleus with an increased atomic number by 1, while the mass number remains unchanged. For instance, arsenic-74 decays to selenium-74 as shown below: \[_{33}^{74}\mathrm{As} \rightarrow _{34}^{74}\mathrm{Se} + \beta^- \]
  • The atomic number increases from 33 to 34, adding one proton.
  • Mass number remains constant.
  • An electron is emitted as a beta particle.
In beta plus decay, a proton is converted into a neutron and a positron, with the positron being expelled from the atom. This decreases the atomic number by 1, with again no change to the mass number. For example, silicon-27 decays into aluminum-27: \[_{14}^{27}\mathrm{Si} \rightarrow _{13}^{27}\mathrm{Al} + \beta^+ \]
  • Silicon loses a proton and emits a positron.
  • The atomic number decreases to 13.
Beta decay plays a crucial role in the management of nuclear reactions, providing insight into the mechanisms of nuclear changes.
Nuclear Physics
Nuclear physics is a branch of physics that studies the components and behavior of atomic nuclei. It encompasses the understanding of radioactive decay, nuclear reactions, and radiation.

Key processes in nuclear physics include:
  • Alpha decay, where a nucleus emits an alpha particle diminishing its atomic number by 2.
  • Beta decay, involving the transformation of neutrons to protons or vice versa through the emission of electrons or positrons.
Nuclear physics is integral to a variety of applications, such as:
  • Energy production through nuclear reactors, utilizing fission and sometimes fusion.
  • Medical treatments like radiation therapy, relying on radioactive isotopes.
  • Industrial applications including radiographic inspection of materials.
By studying nuclear physics, scientists can better understand the forces that hold the nucleus together and develop technologies in various fields, from energy to medicine.

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Most popular questions from this chapter

Gold, \(_{79}^{198} \mathrm{Au}\), undergoes \(\beta^{-}\) decay to an excited state of \(^{198}_{80} \mathrm{Hg}\). If the excited state decays by emission of a photon with energy 0.412 MeV, what is the maximum kinetic energy of the electron emitted in the decay? This maximum occurs when the antineutrino has negligible energy. (The recoil energy of the \(^{198}_{80} \mathrm{Hg}\) nucleus can be ignored. The masses of the neutral atoms in their ground states are 197.968225 u for \(^{198}_{80} \mathrm {Au}\) and 197.966752 u for \(\frac{198}{80} \mathrm{Hg}_{\cdot} \))

Tritium (\(^{3}_{1}\)H) is an unstable isotope of hydrogen; its mass, including one electron, is 3.016049 u. (a) Show that tritium must be unstable with respect to beta decay because the decay products ( \(^{3}_{2}\)He plus an emitted electron ) have less total mass than the tritium. \right. (b) Determine the total kinetic energy (in MeV) of the decay products, taking care to account for the electron masses correctly.

BIO A 70.0-kg person experiences a whole-body exposure to \(\alpha\) radiation with energy 4.77 MeV. A total of \(6.25 \times 10^{12} \alpha\) particles are absorbed. (a) What is the absorbed dose in rad? (b) What is the equivalent dose in rem? (c) If the source is 0.0320 \(\mathrm{g}\) of \(^{226} \mathrm{Ra}\) (half-life 1600 \(\mathrm{y}\)) somewhere in the body, what is the activity of this source? (d) If all the alpha particles produced are absorbed, what time is required for this dose to be delivered?

BIO (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 xays like the one in part (a) would it take to deliver the same total amount of energy to a 75 -kg person as she receives from natural radiation in a year at sea level, as described in part (b)?

As a health physicist, you are being consulted about a spill in a radiochemistry lab. The isotope spilled was 500\(\mu C\) of \(^{131} \mathrm{Ba}\), which has a half-life of 12 days. (a) What mass of \(^{131} \mathrm{Ba}\) was spilled? (b) Your recommendation is to clear the lab until the radiation level has fallen 1.00\(\mu\) Ci. How long will the lab have to be closed?

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