Problem 17 - Chemistry: An Atoms-Focused Approach

Question

The ratio of neutrons to protons in stable nuclei increases with increasing atomic number. Use this trend to explain why multiple \(\alpha\) decay steps in the \(^{238} \mathrm{U}\) decay series are often followed by \(\beta\) decay.

Step-by-Step Solution

Answer

Answer: Multiple alpha decay steps in the Uranium-238 decay series are often followed by beta decay due to the trend of increasing neutron to proton ratio in stable nuclei. As the decay process continues, the nuclei need to reach a more suitable neutron to proton ratio. Beta decay helps the resulting nucleus to achieve a more stable configuration by transforming a neutron into a proton, increasing the atomic number while maintaining the neutron to proton ratio, and providing the required conditions for the stability of the nucleus.

Step 1: Understanding the trend in stable nuclei

For stable nuclei, the ratio of neutrons to protons increases as atomic number increases. This is because of the increasing effect of the electrostatic repulsion between protons in the nucleus. As the atomic number increases, more protons are added to the nucleus and the electrostatic force between them also increases. Hence, more neutrons are required to maintain the balance and keep the nucleus stable.

Step 2: Defining alpha and beta decay

Alpha decay occurs when a nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons (a helium nucleus). When a nucleus undergoes alpha decay, it loses 2 protons and 2 neutrons, resulting in a lower atomic number and mass number. Beta decay occurs when a nucleus transforms a neutron into a proton and emits an electron (beta particle). In this process, the mass number of the nucleus remains unchanged, but the atomic number increases by 1 because a neutron is converted into a proton.

Step 3: The Uranium-238 decay series

The decay series of Uranium-238 involves multiple alpha decay steps followed by beta decay. As Uranium-238 undergoes successive alpha decays, the atomic number and mass number of the resulting nuclei decrease. After each alpha decay, based on specific nuclei properties, the newly formed nucleus may be unstable. Instead of undergoing further alpha decay, the nucleus can undergo beta decay, which increases the atomic number without affecting mass number, in order to reach a more stable configuration.

Step 4: Connecting the trend and decay process

Due to the trend of increasing neutron to proton ratio in stable nuclei, as the decay process continues, the nuclei need to reach a more suitable neutron to proton ratio. Beta decay helps the resulting nucleus to achieve a more stable configuration. By transforming a neutron into a proton, it increases the atomic number while maintaining the neutron to proton ratio, thus providing the required conditions for the stability of the nucleus. This is why multiple alpha decay steps in the Uranium-238 decay series are often followed by beta decay.