/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 A uranium- 235 nucleus decays by... [FREE SOLUTION] | 91Ó°ÊÓ

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A uranium- 235 nucleus decays by a series of alpha and beta emissions until it reaches lead-207. How many alpha emissions and how many beta emissions occur in this series of decays?

Short Answer

Expert verified
7 alpha emissions and 4 beta emissions occur.

Step by step solution

01

Understand the Initial and Final Nuclei

We start with a uranium-235 nucleus, denoted as \( ^{235}_{92}U \), and it decays to lead-207, denoted as \( ^{207}_{82}Pb \). We need to find how many alpha and beta particles are emitted in this decay process.
02

Calculate Total Change in Mass Number

An alpha particle has a mass number of 4, so with each alpha emission, the mass number decreases by 4. The total change in mass number from uranium-235 to lead-207 is \( 235 - 207 = 28 \). So, the total change in mass number corresponds to 28 units.
03

Determine Number of Alpha Emissions

Since each alpha decay reduces the mass number by 4, to achieve a total decrease of 28 in mass number, the number of alpha emissions is \( \frac{28}{4} = 7 \). Thus, there are 7 alpha emissions.
04

Calculate Total Change in Atomic Number

An alpha particle also decreases the atomic number by 2, while a beta particle increases it by 1. From uranium-235 (atomic number 92) to lead-207 (atomic number 82), the total change in atomic number is \( 92 - 82 = 10 \).
05

Determine the Beta Emissions

Since there are 7 alpha emissions, the reduction in atomic number is \( 7 \times 2 = 14 \). To achieve the total reduction of atomic number from uranium to lead, we have \( 14 - x = 10 \), where \( x \) is the increase due to beta emissions. Solving \( 14 - x = 10 \) gives \( x = 4 \). Therefore, there are 4 beta emissions.

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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 common type of nuclear decay, a process by which an unstable atomic nucleus loses energy by releasing energy in the form of alpha particles. An alpha particle is the same as a helium nucleus, comprising 2 protons and 2 neutrons. This means that whenever an atom undergoes alpha decay, its atomic number decreases by 2, and its mass number decreases by 4.

In our exercise, uranium-235 undergoes a series of alpha emissions. This is part of the transformation of heavy elements into more stable ones. As uranium emits an alpha particle:
  • The original uranium isotope ( ^{235}_{92}U ) loses 4 from its mass number, reducing to the final mass number of 207 for lead.
  • The atomic number is reduced by 2 after each emission.
This change is systematic, and in our case, it requires several alpha decays to transform uranium-235 into lead-207, involving 7 such decays in total.
Beta Decay
Beta decay is another form of radioactive decay in which a neutron in the nucleus transforms into a proton and an electron. The electron, known as a beta particle, is emitted from the atom. Unlike alpha particles, beta particles are much lighter. Furthermore, beta decay increases the atomic number by 1 while the mass number remains unchanged.

During beta decay:
  • One neutron is transformed into a proton and an electron.
  • The newly formed electron (beta particle) is emitted from the nucleus.
  • The atomic number of the element increases by 1, but the mass number remains constant.
In our scenario, uranium-235 to lead-207 conversion requires 4 beta emissions. This is essential to adjust the atomic number to coincide with that of lead (82) after accounting for the repeated decrease due to alpha decays.
Uranium-235
Uranium-235 ( ^{235}_{92}U ) is a heavy and unstable isotope of uranium, commonly used in nuclear reactors and weapons due to its ability to sustain a nuclear chain reaction. This isotope contains 92 protons and 143 neutrons.
  • Its instability makes it prone to emit radiation through different decay paths, including alpha and beta decay.
  • Through these processes, uranium-235 eventually becomes a more stable element like lead-207.
  • This decay series is part of a sequence known as a decay chain or radioactive decay series.
The decay of uranium-235 not only provides insights into nuclear physics but also has practical applications, such as in the energy sector and radiometric dating.
Lead-207
Lead-207 ( ^{207}_{82}Pb ) is a stable isotope of lead. It is the result of a long series of radioactive decays starting from heavier parent isotopes like uranium-235.
  • Lead-207 is the endpoint of the decay process that began with uranium-235.
  • As a final product, it is stable, meaning it no longer undergoes radioactive decay.
  • This stable nature makes it useful in different scientific fields, such as geochronology.
Achieving lead-207 from uranium-235 involves multiple steps, as evidenced by the necessity for both alpha and beta decays. Each step brings the uranium nucleus closer to a more stable and less radioactive state.

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