Question

The stable end product in the uranium series $\left({}_{92}^{238}\mathrm{U}\right)$ is (a) ${}_{82}^{205}\mathrm{Pb}$ (b) ${}_{82}^{206}\mathrm{Pb}$ (c) ${}_{82}^{207}\mathrm{Pb}$ (d) ${}_{82}^{208}\mathrm{Pb}$

Short answer

The stable end product in the uranium series ${}_{92}^{238}\mathrm{U}$ is ${}_{82}^{206}\mathrm{Pb}$. So the correct option is (b).

Step-by-step solution

Understanding the Uranium Decay Series

The Uranium 238 decay series refereed as the 'Uranium Series', is a chain of radioactive decays through which the uranium isotope will decay into a series of other isotopes before finally ending up as a stable isotope of lead.

Identifying the final Stable Isotope

In the Uranium Series, the stable end product is Lead-206. During the decay process, the atomic mass number decreases by 32 units (from 238 to 206) while the atomic number decreases by 10 units (from 92 to 82). This is accomplished through a series of alpha and beta minus decays.

Key concepts

Radioactive Decays

Radioactive decay is a natural process where unstable atomic nuclei lose energy by emitting radiation. This process occurs because some combinations of protons and neutrons in the nucleus are not stable. As these unstable nuclei attempt to reach a more stable state, they release energy in the form of particles or electromagnetic waves. There are several different types of decay, but the most common forms are alpha decay, beta decay, and gamma decay.

• In **alpha decay**, the nucleus releases an alpha particle, which consists of two protons and two neutrons. This results in a reduction of the atomic number by 2 and the atomic mass by 4.
• In **beta decay**, a neutron is transformed into a proton with the emission of a beta particle (an electron or positron) and an antineutrino (or neutrino). This changes the atomic number by 1, while the atomic mass remains the same.
• **Gamma decay** involves the release of electromagnetic radiation and typically accompanies other forms of decay, leading to a more stable energy state without changing the atomic number or mass.

Through these processes, the element undergoes a transformation until it becomes stable.

Uranium-238

Uranium-238, denoted as ${}_{92}^{238}\mathrm{U}$, is one of the most common isotopes of uranium. It is not stable and undergoes a series of radioactive decays until it reaches stability. Uranium-238 is abundant in nature and can be found in rocks, soil, and even water.

This isotope is the starting point of the uranium decay series, which consists of 18 different steps. Each step represents a radioactive decay event, transforming the isotope into a different element. Some of these steps include **alpha** and **beta decays**. By going through these decay processes, uranium-238 eventually transforms into a stable isotope of lead (${}_{82}^{206}\mathrm{Pb}$).

Understanding uranium-238's characteristics and its decay path is important in fields like geology and nuclear science, as it provides valuable information about the age and composition of natural materials.

Stable Isotope

In the context of radioactive decay, a stable isotope is one that does not undergo further radioactive decay. These isotopes have a balanced configuration of protons and neutrons, making them energetically stable. After a series of decays, radioactive elements will often transform into a stable state.

In the uranium decay series, uranium-238 ( ${}_{92}^{238}\mathrm{U}$) ends its path as lead-206 (${}_{82}^{206}\mathrm{Pb}$), which is a stable isotope of lead. This transformation occurs through a series of intermediate radioactive elements, with each decay improving the stability of the nucleus until it reaches lead-206. Stable isotopes like lead-206 are significant because they no longer emit radiation, making them safe from a radiological perspective.

Lead-206, as the final stable isotope in the decay series, is a witness to the history and transformations undergone by uranium-238.