Problem 68 - Chemistry and Chemical Reactivity

Question

The last unknown element between bismuth and uranium was discovered by Lise Meitner \((1878-1968)\) and Otto Hahn \((1879-1968)\) in \(1918 .\) They obtained \(^{231} \mathrm{Pa}\) by chemical extraction of pitchblende, in which its concentration is about 1 ppm. This isotope, an \(\alpha\) emitter, has a half- life of \(3.27 \times 10^{4}\) years. (a) Which radioactive decay series (the uranium-235, uranium-238, or thorium-232 series) contains \(^{231} \mathrm{Pa}\) as a member? (b) Suggest a possible sequence of nuclear reactions starting with the long- lived isotope that eventually forms this isotope. (c) What quantity of ore would be required to isolate \(1.0 \mathrm{g}\) of \(^{231} \mathrm{Pa},\) assuming \(100 \%\) yield? (d) Write an equation for the radioactive decay process for \(^{231} \mathrm{Pa}\).

Step-by-Step Solution

Answer

(a) Uranium-235 series. (b) \(^{235}U \rightarrow \alpha + ^{231}Th \rightarrow \beta^- + ^{231}Pa\). (c) 1,000,000 g of ore. (d) \(^{231}Pa \rightarrow ^{227}Ac + \alpha\).

Step 1: Series Identification

To identify which radioactive decay series contains \(^{231} \text{Pa}\), we need to know its origin. \(^{231} \text{Pa}\) is part of the radioactive decay series that begins with \(^{235} \text{U}\). This decay series is known as the uranium-235 series.

Step 2: Identify Reaction Sequence

In the uranium-235 decay series, \(^{231} \text{Pa}\) is formed from \(^{235} \text{U}\). The sequence involves \(^{235} \text{U}\) undergoing alpha decay to form \(^{231} \text{Th}\), which then undergoes beta decay to form \(^{231} \text{Pa}\). The reactions are:1. \(^{235} \text{U} \rightarrow \alpha + ^{231} \text{Th}\)2. \(^{231} \text{Th} \rightarrow \beta^- + ^{231} \text{Pa}\)

Step 3: Calculate Ore Quantity

The concentration of \(^{231} \text{Pa}\) in pitchblende ore is 1 ppm. This means there is 1 gram of \(^{231} \text{Pa}\) per 10⁶ grams of ore. To isolate 1.0 gram of \(^{231} \text{Pa}\), you would need 10⁶ grams (or 1,000,000 grams) of the ore.

Step 4: Write Decay Equation

\(^{231} \text{Pa}\) undergoes alpha decay with a half-life of \(3.27 \times 10^4\) years. This process releases an alpha particle (》He nucleus), producing \(^{227} \text{Ac}\):\(^{231} \text{Pa} \rightarrow ^{227} \text{Ac} + \alpha\)

Key Concepts

Decay Series

Understanding decay series is key to grasping radioactive decay processes. A decay series is a series of radioactive decays that begins with a long-lived parent radionuclide and results in a stable end-product. Each decay leads to the formation of a different element known as a daughter nuclide. This process continues until a stable element is formed. In the case of the uranium-235 decay series, which is relevant to the original exercise, the series begins with the decay of uranium-235 \((^{235}U)\). It moves through several decay steps until it eventually stabilizes. One of the daughters in this series is protactinium-231 \((^{231}Pa)\). For any decay series:

• The series always moves toward greater stability.
• Various particles, like alpha particles and beta particles, are emitted during the transitions.
• Each decay produces a different nuclide until a final, non-radioactive element is reached.

Nuclear Reactions

Nuclear reactions are processes in which atomic nuclei are transformed. They involve a change in the identity or characteristics of an atomic nucleus. These reactions can result in the decay of radioactive elements, leading to transmutation. In the example of protactinium-231 \((^{231}Pa)\) from the original exercise, we see a sequence of nuclear reactions:

• Uranium-235 \((^{235}U)\) undergoes alpha decay, releasing an alpha particle and transforming into thorium-231 \((^{231}Th)\).
• Thorium-231 then undergoes beta decay, converting a neutron into a proton and forming protactinium-231 \((^{231}Pa)\).

Nuclear reactions such as these involve:

• Alpha decay: This is when an alpha particle \(\left( ^4He \right)\) is emitted from the nucleus, reducing the mass number by 4 and the atomic number by 2. \( X \rightarrow Y + \alpha\)
• Beta decay: In this reaction, a neutron in the nucleus is converted to a proton, and an electron (beta particle) is emitted. This increases the atomic number by 1. \( Z \rightarrow W + \beta^- \)

Half-life

One essential concept in radioactive decay is half-life. Half-life is defined as the time required for half of the radioactive nuclei in a sample to decay. It is intrinsic to each radioactive isotope and remains constant over time.In the exercise, protactinium-231 \( \left( ^{231}Pa \right) \) has a half-life of \(3.27 \times 10^4\) years. This vast duration contributes to its persistence in the uranium decay series.Understanding half-life helps us determine:

• The rate at which a substance decays.
• Predicting the behavior of a radioactive sample over time.
• Calculating the age of materials, a principle used in radiometric dating.

For example, if you begin with a 100g sample of \( ^{231}Pa \), after \(3.27 \times 10^4\) years, only 50g would remain due to its half-life. This ongoing reduction continues in a predictable pattern, making half-life a crucial factor in nuclear physics.