Question

Naturally occurring uranium-238 undergoes a radioactive decay series and emits 8 a particles and 6 b particles. What is the stable nucleus at the end of the series?

Short answer

The stable nucleus is Lead-206 (Pb-206).

Step-by-step solution

Understand the Decay Process

Uranium-238 undergoes a series of radioactive decays. It first emits alpha (α) particles. Each alpha particle emission reduces the atomic number by 2 and the mass number by 4.

Calculate the Effect of Alpha Decays

Since 8 alpha particles are emitted, the atomic number decreases by \(8 \times 2 = 16\) and the mass number decreases by \(8 \times 4 = 32\). Starting with uranium-238, \(Z=92\), \(A=238\), the new mass number is \(238 - 32 = 206\), and the new atomic number is \(92 - 16 = 76\).

Understand Beta Decay

Beta (β) decay increases the atomic number by 1, with no change in the mass number. When 6 beta particles are emitted, the atomic number increases by 6.

Calculate the Final Atomic Number

Add the increase from beta decay to the decreased atomic number after alpha decay: \(76 + 6 = 82\).

Identify the Stable Nucleus

An element with an atomic number of 82 and a mass number of 206 is Lead (Pb). Therefore, the stable nucleus at the end of the series is Lead-206.

Key concepts

Uranium-238

Uranium-238 is a naturally occurring isotope of uranium, and it plays a critical role in nuclear science. It is one of the heaviest naturally occurring elements, with an atomic number of 92 and a mass number of 238. This gives it 146 neutrons in its nucleus. Uranium-238 is most well-known for its radioactive properties. It isn't highly radioactive compared to some other isotopes, but it forms the basis of many radioactive decay series. This isotope is significant in geographical dating methods, such as uranium-lead dating. Although uranium-238 is not fissile like its counterpart uranium-235, it can be transformed into plutonium-239, making it crucial for nuclear reactors and weapons research.

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, identical to a helium nucleus. This type of decay is common for heavy elements such as uranium-238. With each alpha decay, the parent nucleus loses two protons and two neutrons:

• The atomic number decreases by 2.
• The mass number decreases by 4.

This change turns the element into a new one as determined by the new atomic number. For uranium-238, emitting 8 alpha particles decreases its atomic number by 16 and mass number by 32, leading to a significantly different element.

Beta Decay

Beta decay is another form of radioactive decay where a neutron in a nucleus converts into a proton, emitting a beta particle in the process. A beta particle is a fast-moving electron or positron, and its emission affects the atomic number: - The atomic number increases by 1 with each beta decay. - The mass number remains unchanged. In our exercise, uranium-238 undergoes beta decay after multiple alpha decays, which resulted in 6 beta particles being emitted. Therefore, beta decay helps stabilize the neutron-to-proton ratio by transforming neutrons into protons, influencing the identity of the resulting element.

Radioactive Series

A radioactive series refers to a sequence of decays an unstable isotope undergoes until it reaches a stable form. Uranium-238 is part of such a series, known as the uranium series or uranium decay chain. - The series begins with uranium-238 and ends with a stable isotope. - Along the way, the isotope undergoes a combination of alpha and beta decays. After emitting 8 alpha and 6 beta particles, uranium-238 finally becomes lead-206, a stable isotope. Understanding these series is crucial in fields like nuclear physics and earth science, as they explain both the behavior of radioactive elements and the formation of stable elements from nuclear processes.