Problem 16 - Chemistry and Chemical Reactivity

Question

The uranium-235 radioactive decay series, beginning with \(_{92}^{235} \mathrm{U}\) and ending with \(_{82}^{207} \mathrm{Pb},\) occurs in the following sequence: \(\alpha, \beta, \alpha, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha .\) Write an equation for each step in this series.

Step-by-Step Solution

Answer

The series starts with \(^{235}_{92}\text{U}\) and ends with \(^{207}_{82}\text{Pb}.\)

Step 1: Understand Decay Processes

In radioactivity, an \(\alpha\) decay reduces the mass number by 4 and the atomic number by 2. A \(\beta\) decay keeps the mass number the same and increases the atomic number by 1.

Step 2: Initial Nuclear Equation

The series starts with \(^{235}_{92}\text{U}.\) We will apply the decay steps sequentially, beginning with \(\alpha\) decay.

Step 3: First Decay (Alpha)

From \(^{235}_{92}\text{U},\) apply \(\alpha\) decay to get \(^{231}_{90}\text{Th}.\)

Step 4: Second Decay (Beta)

From \(^{231}_{90}\text{Th},\) apply \(\beta\) decay to get \(^{231}_{91}\text{Pa}.\)

Step 5: Third Decay (Alpha)

From \(^{231}_{91}\text{Pa},\) apply \(\alpha\) decay to get \(^{227}_{89}\text{Ac}.\)

Step 6: Fourth Decay (Beta)

From \(^{227}_{89}\text{Ac},\) apply \(\beta\) decay to get \(^{227}_{90}\text{Th}.\)

Step 7: Fifth Decay (Alpha)

From \(^{227}_{90}\text{Th},\) apply \(\alpha\) decay to get \(^{223}_{88}\text{Ra}.\)

Step 8: Sixth Decay (Alpha)

From \(^{223}_{88}\text{Ra},\) apply \(\alpha\) decay to get \(^{219}_{86}\text{Rn}.\)

Step 9: Seventh Decay (Alpha)

From \(^{219}_{86}\text{Rn},\) apply \(\alpha\) decay to get \(^{215}_{84}\text{Po}.\)

Step 10: Eighth Decay (Alpha)

From \(^{215}_{84}\text{Po},\) apply \(\alpha\) decay to get \(^{211}_{82}\text{Pb}.\)

Step 11: Ninth Decay (Beta)

From \(^{211}_{82}\text{Pb},\) apply \(\beta\) decay to get \(^{211}_{83}\text{Bi}.\)

Step 12: Tenth Decay (Beta)

From \(^{211}_{83}\text{Bi},\) apply \(\beta\) decay to get \(^{211}_{84}\text{Po}.\)

Step 13: Eleventh Decay (Alpha)

From \(^{211}_{84}\text{Po},\) apply \(\alpha\) decay to reach the endpoint \(^{207}_{82}\text{Pb}.\)

Key Concepts

alpha decay

Alpha decay is a fascinating process in nuclear physics where an unstable nucleus releases an alpha particle. An alpha particle is essentially a helium nucleus, consisting of two protons and two neutrons. This emission leads to two significant changes in the original atom's nucleus:

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

For example, when uranium-235 (\(^{235}_{92}\mathrm{U}\)) undergoes alpha decay, it transforms into thorium-231 (\(^{231}_{90}\mathrm{Th}\)). This process is energetically favorable, as it helps the original element become more stable. Alpha decay is commonly observed in heavy elements like uranium, which have large nuclei

beta decay

Beta decay is another crucial type of radioactive decay in nuclear physics. Unlike alpha decay, beta decay involves the transformation of a neutron into a proton within the nucleus, and the emission of an electron (or \(\beta\) particle). During this process:

• The atomic number increases by 1.
• The mass number remains unchanged.

Consider thorium-231 (\(^{231}_{90}\mathrm{Th}\)) undergoing beta decay. It converts into protactinium-231 (\(^{231}_{91}\mathrm{Pa}\)), due to an increase in the atomic number while maintaining the same mass number. This transition brings the nucleus closer to a more stable configuration. Beta decay is significant in helping balance neutron-to-proton ratios in an atom.

uranium-235 decay

Uranium-235 decay is a process demonstrating a typical radioactive decay series. This specific series begins with uranium-235 (\(^{235}_{92}\mathrm{U}\)) and concludes with lead-207 (\(^{207}_{82}\mathrm{Pb}\)). The journey between these two points involves multiple decays:

• Alpha decays: 8 times, removing mass and reducing the atomic number by 2 each time.
• Beta decays: 3 times, maintaining mass but increasing the atomic number by 1 each time.

In essence, uranium-235 decay reflects the natural transmutation process, gradually transforming into a more stable element. This decay series is critical in nuclear science, as it explains the transformation pathway and energy releases involved.

nuclear reactions

Nuclear reactions encompass the various processes in which the structure of an atom's nucleus changes. These reactions include both natural radioactive decay, like alpha and beta decay, and man-made processes like fission and fusion. Key features of nuclear reactions are:

• Involvement of changes to the nucleus, rather than the electron shell.
• Release or absorption of large amounts of energy.

For uranium-235, nuclear reactions are particularly important. Its decay series is a sequence of reactions leading to transmutation into lead-207. Understanding nuclear reactions helps scientists harness energy safely or use radioactive isotopes in medical, industrial, and research applications.

transmutation

Transmutation refers to the conversion of one element or isotope into another through nuclear reactions, a process intrinsic to radioactive decay series. It occurs naturally, as witnessed in uranium-235 decay where this element steadily transforms into lead-207. Throughout this process:

• Alpha decays reduce atomic mass, shifting the element left on the periodic table.
• Beta decays increase atomic numbers, promoting a shift to the right.

Transmutation exemplifies nature's way of achieving stability through gradual elemental conversion. In human history, the pursuit of controlled transmutation is reflected in the quest for 'alchemy', though today, it's more relevant in understanding nuclear change mechanics. This understanding broadens our grasp of matter's fundamental processes and energy potential.