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Chapter 25: Problem 10

The uranium- 235 radioactive decay series includes 7 alpha emissions and 4 beta emissions. Identify the stable isotope at the end of this series.

Short Answer

Expert verified
The stable isotope is Lead-207 (\( _{82}^{207}Pb \)).

Step by step solution

01

Understand the Basics of Alpha and Beta Decay

Alpha decay results in the release of an alpha particle which consists of 2 protons and 2 neutrons (Helium nucleus), reducing the atomic number by 2 and the mass number by 4. Beta decay involves the conversion of a neutron into a proton, increasing the atomic number by 1 while the mass number remains unchanged.
02

Starting with Uranium-235

Uranium-235, with an atomic number of 92 and a mass number of 235, starts the decay process. Initially, we have \( _{92}^{235}U \) and we must consider the changes due to both alpha and beta decays.
03

Apply 7 Alpha Decays

Each alpha decay decreases the atomic number by 2 and the mass number by 4. For 7 alpha decays, the total change will be a decrease of 14 in atomic number (\( 7 imes 2 \)) and 28 in mass number (\( 7 imes 4 \)). This results in an atomic number of \( 92 - 14 = 78 \) and a mass number of \( 235 - 28 = 207 \).
04

Apply 4 Beta Decays

Each beta decay increases the atomic number by 1. For 4 beta decays, this results in an additional increase of 4 in the atomic number. Therefore, the new atomic number becomes \( 78 + 4 = 82 \). The mass number remains unchanged at 207 after beta decays.
05

Determine the Final Isotope

With a final atomic number of 82 and a mass number of 207, we identify the element on the periodic table. The element with atomic number 82 is Lead (Pb). Therefore, the final isotope is \( _{82}^{207}Pb \).

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Key Concepts

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

Uranium-235
Uranium-235 is a crucial isotope used in nuclear physics and energy applications. It is one of the three natural isotopes of uranium, distinguished by its mass number of 235. Uranium-235 is particularly notable because it is fissile, meaning it can sustain a nuclear chain reaction. This property is what enables it to be used as fuel in nuclear reactors and nuclear weapons.

Some key features of uranium-235 include:
  • Half-life: 703.8 million years
  • Natural abundance: Approximately 0.72% of all uranium found on Earth
  • Decay products: It undergoes a series of radioactive decays to eventually become a stable isotope
In its decay series, uranium-235 emits alpha and beta particles, which gradually transform it into different elements until it reaches a stable state.
Alpha Decay
Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle. An alpha particle consists of 2 protons and 2 neutrons, the same as a helium nucleus. During alpha decay, the atomic number of an element decreases by 2, and its mass number decreases by 4, effectively changing the element into a lighter element.

For instance, when uranium-235 undergoes alpha decay, it emits an alpha particle, transforming into a different element with two fewer protons on the periodic table.
  • Reduces atomic number: By 2
  • Reduces mass number: By 4
  • Emitted particle: Helium nucleus (alpha particle)
Alpha decay is a common mode of decay for heavy elements, helping to stabilize large nuclei by decreasing their size.
Beta Decay
Beta decay is another form of radioactive decay, but unlike alpha decay, it involves the transformation of a neutron into a proton inside the nucleus. This process increases the atomic number by 1, while the mass number stays the same. As a result, a new element forms, moving the original element one place up on the periodic table.

Beta decay can increase the stability of a nucleus by converting an excess neutron into a proton:
  • Increases atomic number: By 1
  • Keeps mass number: Unchanged
  • Emitted particle: Electron or beta particle
During the uranium-235 decay series, beta decay helps adjust the neutron-to-proton ratio, making the nucleus more stable as it transitions to different elements.
Stable Isotope
A stable isotope is the end goal of the radioactive decay series. It is an isotope that does not undergo radioactive decay and remains constant over time. For uranium-235, after undergoing a series of alpha and beta decays, the final product is a stable isotope.

In the decay series of uranium-235, it ultimately becomes lead-207, a stable isotope with the following characteristics:
  • Atomic number: 82 (lead)
  • Mass number: 207
  • Stability: It no longer undergoes radioactive decay
Reaching a stable isotope marks the completion of the radioactive decay series, where the original radionuclide transforms into a non-radioactive form, concluding its journey of emission and transformation.

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Most popular questions from this chapter

Radon has been the focus of much attention recently because it is often found in homes. Radon-222 emits \(\alpha\) particles and has a half-life of 3.82 days. (a) Write a balanced equation to show this process. (b) How long does it take for a sample of \(^{222} \mathrm{Rn}\) to decrease to \(20.0 \%\) of its original activity?

Radioactive cobalt-60 is used extensively in nuclear medicine as a \(\gamma\) -ray source. It is made by a neutron capture reaction from cobalt-59 and is a \(\beta\) emitter; \(\beta\) emission is accompanied by strong \(\gamma\) radiation. The half-life of cobalt-60 is 5.27 years. (a) How long will it take for a cobalt- 60 source to decrease to one eighth of its original activity? (b) What fraction of the activity of a cobalt-60 source remains after 1.0 year?

There are two isotopes of americium, both with half-lives sufficiently long to allow the handling of large quantities. Americium-241, with a half-life of 432 years, is an \(\alpha\) emitter used in smoke detectors. The isotope is formed from \(^{239} \mathrm{Pu}\) by absorption of two neutrons followed by emission of a \(\beta\) particle. Write a balanced equation for this process.

The fission of uranium- 235 releases \(2 \times 10^{10} \mathrm{kJ} /\) mol. Calculate the quantity of mass converted to energy in this process.

Some of the reactions explored by Ernest Rutherford (pages 67 and 1166 ) and others are listed below. Identify the unknown species in each reaction. (a) \(^{14} \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow^{17}_{8} \mathrm{O}+?\) (b) \(^{9}_{4} \mathrm{Be}+_{2}^{4} \mathrm{He} \longrightarrow ?+\\_{1}^{6} \mathrm{n}\) (c) \(?+\\_{4}^{2} \mathrm{He} \longrightarrow_{15}^{30} \mathrm{P}+\\_{1}^{0} \mathrm{n}\) (d) \(^{233} \mathrm{Pu}+_{2}^{4} \mathrm{He} \longrightarrow ?+\\_{1}^{0} \mathrm{n}\)
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