Problem 67 - Chemistry

Question

In the bismuth-214 natural decay series, Bi-214 initially undergoes \(\beta\) decay, the resulting daughter emits an \(\alpha\) particle, and the succeeding daughters emit a \(\beta\) and a \(\beta\) particle in that order. Determine the product of each step in the Bi-214 decay series.

Step-by-Step Solution

Answer

The products of each step in the Bi-214 decay series are: \(Bi-214 \rightarrow Po-214 \rightarrow Pb-210 \rightarrow Bi-210 \rightarrow Po-210\).

Step 1: Bi-214 β- decay

In this step, Bi-214 undergoes β- decay, which means one neutron is converted into a proton and an electron is emitted. To conserve the number of protons and neutrons, the resulting daughter nuclide will have one more proton and one fewer neutron. Bi-214 has 83 protons, so since one neutron converts to a proton, the new nuclide will have 84 protons: Bi-214 (Z=83, A=214) -> Daughter nuclide (Z=84, A=214) Checking the periodic table, an element with 84 protons is Polonium (Po). Thus, the daughter nuclide is Po-214.

Step 2: Po-214 α decay

In this step, Po-214 emits an α particle, which is comprised of 2 protons and 2 neutrons. To conserve the number of protons and neutrons, the daughter nuclide will have 2 fewer protons and 2 fewer neutrons: Po-214 (Z=84, A=214) -> Daughter nuclide (Z=82, A=210) Checking the periodic table, an element with 82 protons is Lead (Pb). Thus, the daughter nuclide is Pb-210.

Step 3: Pb-210 β- decay

In this step, Pb-210 undergoes β- decay, converting one neutron to a proton and emitting an electron. The resulting daughter nuclide will have one more proton and one fewer neutron: Pb-210 (Z=82, A=210) -> Daughter nuclide (Z=83, A=210) Checking the periodic table, an element with 83 protons is Bismuth (Bi). Thus, the daughter nuclide is Bi-210.

Step 4: Bi-210 β- decay

In this final step, Bi-210 undergoes another β- decay, again converting a neutron into a proton and emitting an electron. The resulting daughter nuclide will have one more proton and one fewer neutron: Bi-210 (Z=83, A=210) -> Daughter nuclide (Z=84, A=210) Checking the periodic table, an element with 84 protons is Polonium (Po). Thus, the final daughter nuclide is Po-210. In conclusion, the Bi-214 decay series consists of the following products: 1. Bi-214 -> Po-214 2. Po-214 -> Pb-210 3. Pb-210 -> Bi-210 4. Bi-210 -> Po-210

Key Concepts

Beta Decay

Beta decay is an interesting process that involves the transformation of a neutron into a proton, or vice versa, within an atomic nucleus. This process results in the emission of a beta particle, which can be an electron ( \( \beta^- \) decay) or a positron ( \( \beta^+ \) decay). In the context of the Bi-214 decay series, we focus on \( \beta^- \) decay, where an electron is emitted.

Here's what happens during \( \beta^- \) decay:

• One neutron in the nucleus converts into a proton.
• An electron, known as a beta particle, is emitted from the nucleus.
• This results in an increase in the atomic number since there is one more proton.

For the Bi-214 decay series, the atomic number of bismuth goes from 83 to 84, transforming it into polonium-214 (Po-214).

Understanding beta decay is vital for grasping how elements transform into their daughter products in radioactive series.

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle. An alpha particle consists of two protons and two neutrons, equivalent to the nucleus of a helium atom. This process reduces the atomic number by 2 and the mass number by 4, turning the parent atom into a different element.

During the alpha decay of Po-214 in the bismuth-214 decay series:

• The number of protons decreases by two.
• The number of neutrons decreases by two, too.
• The daughter nuclide is lead-210 (Pb-210), as the atomic number shifts from 84 to 82.

Alpha decay is significant as it initiates a change in the identity of the element itself, leading to the formation of a progeny element. It's crucial for understanding the alteration of atomic nuclei in nuclear decay series.

Radioactive Decay Process

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. Understanding this process means diving into a sequence of transformations that leads to stability over time.

In the Bi-214 decay series:

• It begins with beta decay, shifting from Bi-214 to Po-214.
• This is followed by alpha decay, transforming Po-214 to Pb-210.
• Subsequent beta decays return Pb-210 to Bi-210 and finally back to Po-210.

Such decay series are essential to comprehend how elements spontaneously transform to attain stable configurations. As the series proceeds through different forms of decay, the nucleus of the atom gradually arrives at a stable state, often resulting in the production of a stable, non-radioactive element.

The radioactive decay process elucidates the foundational principles of nuclear chemistry and physics, showcasing how substances evolve at an atomic level.