Problem 17 - Chemistry and Chemical Reactivity

Question

The thorium-232 radioactive decay series, beginning with \(^{232}_{90}\)Th and ending with \(^{208}_{82}\)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

Thorium-232 decays to lead-208 after 10 decays: 5 alpha and 4 beta processes.

Step 1: Understanding Alpha Decay

An alpha decay reduces the atomic number by 2 and the mass number by 4. This happens because an alpha particle consists of 2 protons and 2 neutrons (He nucleus) being emitted.

Step 2: Atomic and Mass Numbers after First Alpha Decay

Starting from thorium-232, the nucleus undergoes an alpha decay: \[^{232}_{90}\text{Th} \rightarrow ^{228}_{88}\text{Ra} + \alpha\]The thorium-232 element loses an alpha particle.

Step 3: Understanding Beta Decay

A beta decay results in an increase of the atomic number by 1, while the mass number remains unchanged. This occurs because a neutron is converted to a proton and an electron (beta particle) is emitted.

Step 4: Atomic and Mass Numbers after First Beta Decay

With a beta decay, the atomic number increases by 1:\[^{228}_{88}\text{Ra} \rightarrow ^{228}_{89}\text{Ac} + \beta\]The radium turns into actinium by emitting a beta particle.

Step 5: Atomic and Mass Numbers after Second Beta Decay

The actinium nucleus undergoes another beta decay:\[^{228}_{89}\text{Ac} \rightarrow ^{228}_{90}\text{Th} + \beta\]Actinium changes back to thorium via beta decay.

Step 6: Atomic and Mass Numbers after Second Alpha Decay

Another alpha decay reduces the atomic number by 2 and the mass number by 4:\[^{228}_{90}\text{Th} \rightarrow ^{224}_{88}\text{Ra} + \alpha\]The thorium changes to radium by emitting the alpha particle.

Step 7: Atomic and Mass Numbers after Third Alpha Decay

Continue with an alpha decay on radium:\[^{224}_{88}\text{Ra} \rightarrow ^{220}_{86}\text{Rn} + \alpha\]Radium changes to radon via alpha decay.

Step 8: Atomic and Mass Numbers after Fourth Alpha Decay

Followed by another alpha decay on radon:\[^{220}_{86}\text{Rn} \rightarrow ^{216}_{84}\text{Po} + \alpha\]Radon changes to polonium by emitting an alpha particle.

Step 9: Atomic and Mass Numbers after Fifth Alpha Decay

Polonium undergoes an alpha decay:\[^{216}_{84}\text{Po} \rightarrow ^{212}_{82}\text{Pb} + \alpha\]The element is now lead-212.

Step 10: Atomic and Mass Numbers after Third Beta Decay

Lead undergoes a beta decay:\[^{212}_{82}\text{Pb} \rightarrow ^{212}_{83}\text{Bi} + \beta\]Lead changes to bismuth by a beta particle emission.

Step 11: Atomic and Mass Numbers after Fourth Beta Decay

Bismuth undergoes another beta decay:\[^{212}_{83}\text{Bi} \rightarrow ^{212}_{84}\text{Po} + \beta\]This results in a polonium nucleus once again.

Step 12: Final Alpha Decay to Lead-208

Finally, polonium undergoes an alpha decay:\[^{212}_{84}\text{Po} \rightarrow ^{208}_{82}\text{Pb} + \alpha\]This brings the sequence to completion with stable lead-208.

Key Concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle is made up of 2 protons and 2 neutrons. This is equivalent to a helium nucleus.When an atom undergoes alpha decay, it loses an alpha particle which causes:

• A decrease in the atomic number by 2
• A decrease in the mass number by 4

For example, when thorium-232 decays by alpha emission, it transforms into radium-228:\[^{232}_{90}\text{Th} \rightarrow ^{228}_{88}\text{Ra} + \alpha\]This process shows how the thorium loses an alpha particle, reducing the number of protons and neutrons in its nucleus. As a result, thorium changes to a completely different element—radium.

Beta Decay

Beta decay is another form of radioactive transformation. During beta decay, a neutron in the nucleus is converted into a proton, and an electron, known as a beta particle, is emitted. This results in:

• An increase in the atomic number by 1
• The mass number remains the same

As an example, consider the process of radium-228 undergoing beta decay to turn into actinium-228:\[^{228}_{88}\text{Ra} \rightarrow ^{228}_{89}\text{Ac} + \beta\]Here, no change in the overall mass number occurs, but the atomic number increases as a neutron becomes a proton. This changes the element from radium to actinium, indicating how beta decay contributes to the transformation of elements in a decay series.

Thorium Decay Series

The thorium decay series is a sequence of radioactive decay steps starting with a parent isotope, thorium-232, and ending with a stable isotope, lead-208. This sequence provides a fascinating pathway of how a single radioactive element transmutes into different elements through a sequence of alpha and beta decays.In the thorium series, the decay process includes:

• Multiple alpha decays, each reducing the atomic number and the mass number
• Several beta decays, increasing the atomic number without changing the mass

By following the series, you will see changes like:\[^{232}_{90}\text{Th}\rightarrow ^{228}_{88}\text{Ra} + \alpha \rightarrow ^{228}_{89}\text{Ac} + \beta \rightarrow \text{...}\rightarrow ^{208}_{82}\text{Pb}\]This specific order showcases how thorium eventually evolves into stable lead after undergoing a defined number of nuclear transformations.

Nuclear Reactions

Nuclear reactions concern changes within an atom's nucleus and involve remarkable transformations that significantly alter energy levels and elemental identities. In the context of radioactive decay, nuclear reactions illustrate how unstable isotopes achieve stability through these transformations. Consider the types of nuclear reactions involved in a decay series:

• Alpha decay leads to significant shifts as the atom loses a substantial part of its nucleus (2 protons and 2 neutrons)
• Beta decay subtly modifies the proton/neutron composition, adding a proton and eliminating a neutron

Through these reactions in the thorium decay series, each step represents a transformation leading to greater nuclear stability. This demonstrates the profound changes these nuclear reactions impose on elements, showcasing the natural process of reaching a stable, non-radioactive state.