Problem 25 - Chemistry and Chemical Reactivity

Question

The uranium- 235 radioactive decay series, beginning with \(^{235}_{92} \mathrm{U}\) and ending with \(^{207}_ {82} \mathrm{Pb}\) 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

U-235 decays to Pb-207 through a sequence of alpha and beta decays.

Step 1: Understanding Alpha Decay

In alpha decay, an alpha particle, consisting of 2 protons and 2 neutrons, is emitted from the nucleus. This means the atomic mass decreases by 4 and the atomic number decreases by 2. Now, let's perform the first decay starting from uranium-235: \[ ^{235}_{92} \mathrm{U} \to ^{231}_{90} \mathrm{Th} + ^{4}_{2} \alpha \]

Step 2: Applying Beta Decay

In beta decay, a neutron is converted into a proton, which increases the atomic number by 1, but the mass number remains unchanged. Now, apply beta decay to thorium-231:\[ ^{231}_{90} \mathrm{Th} \to ^{231}_{91} \mathrm{Pa} + \beta \]

Step 3: Alpha Decay Again

Next, perform another alpha decay on protactinium-231:\[ ^{231}_{91} \mathrm{Pa} \to ^{227}_{89} \mathrm{Ac} + ^{4}_{2} \alpha \]

Step 4: Another Beta Decay

The following decay is a beta decay on actinium-227:\[ ^{227}_{89} \mathrm{Ac} \to ^{227}_{90} \mathrm{Th} + \beta \]

Step 5: A Series of Alpha Decays

Sequential alpha decays will occur as follows:1. Thorium-227 undergoes alpha decay: \[ ^{227}_{90} \mathrm{Th} \to ^{223}_{88} \mathrm{Ra} + ^{4}_{2} \alpha \] 2. Radium-223 undergoes alpha decay: \[ ^{223}_{88} \mathrm{Ra} \to ^{219}_{86} \mathrm{Rn} + ^{4}_{2} \alpha \] 3. Radon-219 undergoes another alpha decay: \[ ^{219}_{86} \mathrm{Rn} \to ^{215}_{84} \mathrm{Po} + ^{4}_{2} \alpha \] 4. Polonium-215 undergoes the final alpha decay in this sequence: \[ ^{215}_{84} \mathrm{Po} \to ^{211}_{82} \mathrm{Pb} + ^{4}_{2} \alpha \]

Step 6: Beta Decay Sequence

After series of alpha decay, apply two consecutive beta decays:1. Lead-211 undergoes beta decay: \[ ^{211}_{82} \mathrm{Pb} \to ^{211}_{83} \mathrm{Bi} + \beta \] 2. Bismuth-211 undergoes another beta decay: \[ ^{211}_{83} \mathrm{Bi} \to ^{211}_{84} \mathrm{Po} + \beta \]

Step 7: Final Alpha Decay

The final step is an alpha decay of polonium-211:\[ ^{211}_{84} \mathrm{Po} \to ^{207}_{82} \mathrm{Pb} + ^{4}_{2} \alpha \] Now, we have completed the decay series ending with lead-207.

Key Concepts

Alpha Decay

In an alpha decay process, an unstable nucleus releases an alpha particle to stabilize itself. An alpha particle is made up of 2 protons and 2 neutrons, similar to a helium nucleus. When a nucleus undergoes alpha decay, it loses these four nucleons, causing its atomic mass to decrease by 4 and the atomic number to fall by 2.
For example, when uranium-235 ( ^{235}_{92} ext{U}) undergoes alpha decay, it transforms into thorium-231 ( ^{231}_{90} ext{Th}). This change reflects the loss of 2 protons, moving the element from position 92 to 90 on the periodic table. Thus:

• The mass number is reduced by 4: from 235 to 231
• The atomic number is reduced by 2: from 92 to 90

Alpha decay is common among heavy nuclei, as releasing an alpha particle helps in attaining a more stable energy state.

Beta Decay

Beta decay involves the transformation of a neutron into a proton within an atomic nucleus. This transformation results in the emission of a beta particle, which is essentially an electron or positron, depending on the decay type.
In the case of a beta minus decay, a neutron converts to a proton while releasing a beta-minus particle, an electron, and an antineutrino. This chain of events increases the atomic number by 1 while the mass number remains the same, altering the element to the next one on the periodic table. For instance, when thorium-231 ( ^{231}_{90} ext{Th}) decays by beta emission, it becomes protactinium-231 ( ^{231}_{91} ext{Pa}):

• The mass number remains 231.
• The atomic number increases by 1, from 90 to 91.

Thus, beta decay allows an unstable nucleus to adjust its ratio of protons to neutrons, achieving greater stability.

Uranium-235 Decay

Uranium-235 ( ^{235}_{92} ext{U}) is a notable isotope of uranium that undergoes a series of radioactive decays leading to a stable form. This decay series is called the uranium-235 decay series and involves various transformations, including both alpha and beta decays, ultimately resulting in lead-207 ( ^{207}_{82} ext{Pb}).
Throughout its decay pathway:

• Alpha decay reduces both the mass and atomic numbers, reshaping the element's identity.
• Beta decay alters the atomic number while keeping the mass number stable, facilitating the creation of other elements in the decay chain.

This series is profoundly significant in nuclear physics and geochronology, helping scientists reach insights into the Earth's natural history and energy generation processes.

Nuclear Reactions

Nuclear reactions involve changes within an atomic nucleus, leading to various transformations and the emission of radiation. Unlike chemical reactions, where electrons are shared or transferred among atoms, nuclear reactions directly change the nucleus's composition, impacting mass and energy on an atomic level.
These reactions play a pivotal role in the life cycle of stars and the existence of elements. In nuclear reactions:

• Alpha reactions involve large changes, as observed with heavy elements releasing helium nuclei.
• Beta reactions reflect smaller changes, with neutrons converting into protons and vice versa.

Nuclear reactions underpin diverse phenomena, from nuclear power generation to medical applications and environmental studies. They provide insights into the fundamental forces governing atomic interactions and allow for technological and scientific advancements.