Problem 26 - Chemistry and Chemical Reactivity

Question

The thorium- 232 radioactive decay series, beginning with \(^{232}_{90} \mathrm{TH}\) and ending with \(^{208}_{82} \mathrm{Pb}\) occurs in the following sequence: \(\alpha, \beta, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha\) Write an equation for each step in this series.

Step-by-Step Solution

Answer

The decay series results in stable lead-208.

Step 1: Initial Thorium Decay

The sequence starts with the decay of thorium-232 by alpha emission. Each alpha decay reduces the mass number by 4 and the atomic number by 2. Therefore, thorium-232 (^{232}_{90} ext{Th}) loses an alpha particle (^4_2 ext{He}), transforming into radium-228 (^{228}_{88} ext{Ra}). The equation is:\[ ^{232}_{90} ext{Th} ightarrow ^{228}_{88} ext{Ra} + ^{4}_{2} ext{He}. \]

Step 2: First Beta Decay

Radium-228 undergoes beta decay, where a neutron converts into a proton, increasing the atomic number by 1 while the mass number remains unchanged. It transforms into actinium-228 (^{228}_{89} ext{Ac}). The equation is:\[ ^{228}_{88} ext{Ra} ightarrow ^{228}_{89} ext{Ac} + ^0_{-1} e. \]

Step 3: Second Beta Decay

Actinium-228 then undergoes another beta decay similarly, transforming into thorium-228 (^{228}_{90} ext{Th}). The equation is:\[ ^{228}_{89} ext{Ac} ightarrow ^{228}_{90} ext{Th} + ^0_{-1} e. \]

Step 4: Second Alpha Decay

Thorium-228 undergoes alpha decay to form radium-224 (^{224}_{88} ext{Ra}). The equation is:\[ ^{228}_{90} ext{Th} ightarrow ^{224}_{88} ext{Ra} + ^{4}_{2} ext{He}. \]

Step 5: Third Alpha Decay

Radium-224 then decays by emitting an alpha particle and forms radon-220 (^{220}_{86} ext{Rn}). The equation is:\[ ^{224}_{88} ext{Ra} ightarrow ^{220}_{86} ext{Rn} + ^{4}_{2} ext{He}. \]

Step 6: Fourth Alpha Decay

Continuing with the sequence, radon-220 undergoes alpha decay, producing polonium-216 (^{216}_{84} ext{Po}). The equation is:\[ ^{220}_{86} ext{Rn} ightarrow ^{216}_{84} ext{Po} + ^{4}_{2} ext{He}. \]

Step 7: Fifth Alpha Decay

Polonium-216 decays via alpha emission, becoming lead-212 (^{212}_{82} ext{Pb}). The equation is:\[ ^{216}_{84} ext{Po} ightarrow ^{212}_{82} ext{Pb} + ^{4}_{2} ext{He}. \]

Step 8: Third Beta Decay

Lead-212 undergoes beta decay, producing bismuth-212 (^{212}_{83} ext{Bi}). The equation is:\[ ^{212}_{82} ext{Pb} ightarrow ^{212}_{83} ext{Bi} + ^0_{-1} e. \]

Step 9: Fourth Beta Decay

The bismuth-212 created subsequently undergoes beta decay to form polonium-212 (^{212}_{84} ext{Po}). The equation is:\[ ^{212}_{83} ext{Bi} ightarrow ^{212}_{84} ext{Po} + ^0_{-1} e. \]

Step 10: Final Alpha Decay

Finally, polonium-212 undergoes one last alpha decay, resulting in the stable lead-208 (^{208}_{82} ext{Pb}). The equation is:\[ ^{212}_{84} ext{Po} ightarrow ^{208}_{82} ext{Pb} + ^{4}_{2} ext{He}. \]

Key Concepts

Alpha Decay

Alpha decay is a process where an unstable nucleus releases an alpha particle, which consists of 2 protons and 2 neutrons. This emission results in a decrease in the atomic number by 2 and the mass number by 4. Imagine it like the nucleus shedding a tiny piece of itself, making it slightly lighter and changing its identity to a different element.

• An alpha particle is identical to a helium nucleus with a composition of two protons and two neutrons.
• The reduction in atomic number causes the element to shift two places back in the periodic table.
• Alpha decay is common in heavy elements, such as uranium and thorium, which tend to have more protons than their structures can comfortably hold.

Through each step in a decay series, like the thorium decay series, alpha decay allows the original heavy nucleus to transition into a more stable state, eventually forming a stable element like lead.

Beta Decay

In beta decay, a neutron in an unstable nucleus is transformed into a proton, releasing a beta particle, which is a fast-moving electron. This process increases the atomic number by 1, while the mass number stays the same. It may sound like magic, but it's actually the conversion of one type of subatomic particle into another.

• This occurs because a neutron is composed of one proton and one electron-like entity, where changes take place.
• When a beta particle is emitted, the element transforms to the next one on the periodic table.
• Beta decay is a common way for isotopes to become more stable, as it helps in balancing the ratio of neutrons to protons.

Throughout the radioactive decay series of thorium, beta decay plays a crucial role in maintaining the chain's progression by altering the atomic identity of the isotopes involved.

Thorium

Thorium is a naturally occurring radioactive element and is particularly known for being the starting point of the thorium decay series. Labeled with the atomic number 90, thorium is heavier than lead and undergoes alpha decay processes to eventually become a stable lead isotope.

• As a member of the actinide series, thorium has a significant role in nuclear physics due to its radioactive properties.
• Its most stable form, thorium-232, is an important subject of study in nuclear science and energy generation potential.
• Over time, thorium-232 decays through a series of transformations, eventually stabilizing into lead-208.

Understanding thorium's characteristics helps grasp its journey through various decays until it becomes part of a stable lead isotope.

Lead

Lead is the end-product of many decay series, including the thorium series. Known for its stability, lead does not undergo any spontaneous radioactive decay itself, making it the final, resting element in the decay chain.

• Lead appears at the end of the thorium decay series as lead-208, a stable isotope resistant to further radioactive decay.
• This heavy metal, with atomic number 82, is entirely stable and won't change unless through artificial means.
• The transformation into lead represents the journey from a radioactive state to stability, making lead an important marker for the completion of a radioactive decay series.

Lead's presence at the end of decay sequences ensures the stabilization of the original radioactive elements, allowing them to exist in equilibrium without further transformation.

Actinium

Actinium is a rare and radioactive element that also finds a temporary place in the thorium decay series. With the atomic number 89, actinium highlights the complex journey of nuclear transformations.

• Actinium is notable for its intense radioactivity and its role as an intermediate state in decay chains.
• It quickly undergoes further transformations, largely through beta decay, showcasing its ephemeral nature as it transitions between isotopes.
• Being part of the actinide series, actinium helps to piece together the pathway from thorium-232 to stable lead-208.

The presence of actinium in decay pathways emphasizes the importance of transient states in the completion of natural element transformations.