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Chapter 29: Problem 22

Thorium-232 ( \(^{232}\) Th) decays via \(\alpha\) decay. Write out the reaction and identify the daughter nuclide.

Short Answer

Expert verified
Answer: The daughter nuclide formed is Radium-228 (\(^{228}\)Ra).

Step by step solution

01

Understanding Alpha Decay

Alpha decay is a radioactive decay process in which an unstable nucleus emits an alpha particle, made of 2 protons and 2 neutrons; so it is a helium-4 nucleus (\(^4_2\)He). This leads to the formation of a new nucleus that has 2 less protons and 2 less neutrons than the original nucleus.
02

Write the Initial Nuclide

The given nuclide is Thorium-232 (\(^{232}\)Th). This implies that it has 232 nucleons (protons and neutrons), and since it is Thorium, it has an atomic number of 90 (90 protons). Therefore, the initial nuclide can be represented as \(^{232}_{90}\)Th.
03

Represent the Alpha Particle

As mentioned in Step 1, an alpha particle is equivalent to a helium-4 nucleus, with 2 protons and 2 neutrons. Thus, we can write the alpha particle as \(^4_2\)He.
04

Write the Alpha Decay Reaction

During alpha decay, the initial nuclide emits the alpha particle. To write the reaction, place the initial nucleus, the alpha particle, and the daughter nucleus side by side, maintaining the conservation of mass number (number of nucleons) and conservation of atomic number (number of protons). The alpha decay reaction would look like: \(^{232}_{90}\)Th \(\rightarrow\) \(^4_2\)He + Daughter Nuclide
05

Determine the Daughter Nuclide

To determine the daughter nuclide, subtract the mass number and atomic number of the alpha particle from the mass number and atomic number of the initial Thorium-232 nucleus, respectively: Mass number: \(232 - 4 = 228\) Atomic number: \(90 - 2 = 88\) Now, the daughter nucleus has a mass number of 228 and an atomic number of 88, which corresponds to the element Radium (Ra). Therefore, the daughter nuclide is \(^{228}_{88}\)Ra.
06

Write the Complete Alpha Decay Reaction

Now that we have the daughter nuclide, we can write the complete alpha decay reaction: \(^{232}_{90}\)Th \(\rightarrow\) \(^4_2\)He + \(^{228}_{88}\)Ra The daughter nuclide is Radium-228 (\(^{228}\)Ra).

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Most popular questions from this chapter

The radioactive decay of \(^{238} \mathrm{U}\) produces \(\alpha\) particles with a kinetic energy of \(4.17 \mathrm{MeV} .\) (a) At what speed do these \(\alpha\) particles move? (b) Put yourself in the place of Rutherford and Geiger. You know that \(\alpha\) particles are positively charged (from the way they are deflected in a magnetic field). You want to measure the speed of the \(\alpha\) particles using a velocity selector. If your magnet produces a magnetic field of \(0.30 \mathrm{T},\) what strength electric field would allow the \(\alpha\) particles to pass through undeflected? (c) Now that you know the speed of the \(\alpha\) particles, you measure the radius of their trajectory in the same magnetic field (without the electric field) to determine their charge-to-mass ratio. Using the charge and mass of the \(\alpha\) particle, what would the radius be in a \(0.30-\mathrm{T}\) field? (d) Why can you determine only the charge-to-mass ratio \((q / m)\) by this experiment, but not the individual values of \(q\) and \(m ?\)
A neutron star is a star that has collapsed into a collection of tightly packed neutrons. Thus, it is something like a giant nucleus; but since it is electrically neutral, there is no Coulomb repulsion to break it up. The force holding it together is gravity. Suppose the Sun were to collapse into a neutron star. What would its radius be? Assume that the density is about the same as for a nucleus. Express your answer in kilometers.
In naturally occurring potassium, \(0.0117 \%\) of the nuclei are radioactive \(^{40} \mathrm{K} .\) (a) What mass of \(^{40} \mathrm{K}\) is found in a broccoli stalk containing \(300 \mathrm{mg}\) of potassium? (b) What is the activity of this broccoli stalk due to \(^{40} \mathrm{K} ?\)
How many neutrons are found in a \(^{35} \mathrm{Cl}\) nucleus?
The carbon isotope \({ }^{15} \mathrm{C}\) decays much faster than ${ }^{14} \mathrm{C}$. (a) Using Appendix B, write a nuclear reaction showing the decay of ${ }^{15} \mathrm{C}\(. (b) How much energy is released when \){ }^{15} \mathrm{C}$ decays?
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