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?

Verified step by step guidance

1. Identify the type of particles emitted during the decay series. In this case, uranium-238 emits 8 alpha ( ext{a}) particles and 6 beta ( ext{b}) particles.
2. Understand that each alpha particle emission reduces the atomic number by 2 and the mass number by 4. Calculate the new atomic number and mass number after the emission of 8 alpha particles.
3. Recognize that each beta particle emission increases the atomic number by 1 (with no change in mass number) as a neutron in the nucleus converts to a proton. Calculate the final atomic number after the emission of 6 beta particles.
4. Combine the changes in atomic and mass numbers to find the new element in the periodic table that corresponds to these numbers. This element is the stable nucleus at the end of the decay series.
5. Verify the stability of the resulting nucleus by checking if it is known to be stable and does not undergo further radioactive decay.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha (α) and beta (β) decay. In alpha decay, the nucleus emits an alpha particle, which consists of two protons and two neutrons, while beta decay involves the transformation of a neutron into a proton with the emission of a beta particle (an electron or positron).

Alpha and Beta Particles

Alpha particles are positively charged and consist of two protons and two neutrons, effectively reducing the atomic number of the parent nucleus by two and the mass number by four. Beta particles, on the other hand, are high-energy, high-speed electrons or positrons emitted from a decaying nucleus, which increases the atomic number by one while keeping the mass number unchanged. Understanding these emissions is crucial for determining the final stable nucleus after decay.

Decay Series and Stability

A decay series is a sequence of radioactive decays that a particular isotope undergoes until it reaches a stable isotope. Each decay step alters the atomic and mass numbers, leading to different isotopes. The stability of the final nucleus is determined by its position on the nuclear stability curve, where isotopes with a balanced ratio of protons to neutrons are more stable. In the case of uranium-238, the series ultimately leads to a stable isotope of lead.