Problem 12 - College Physics

Question

Polonium-214 can decay by alpha decay. (a) The product of its decay has how many fewer protons than polonium- 214:(1) zero, (2) one, (3) two, or (4) four? (b) Write the nuclear equation for this decay and determine the daughter nucleus.

Step-by-Step Solution

Answer

(a) Two fewer protons. (b) Daughter nucleus: Lead-210.

Step 1: Understanding Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable atom loses an alpha particle. An alpha particle consists of 2 protons and 2 neutrons. As a result, when an atom undergoes alpha decay, it loses 2 protons and 2 neutrons.

Step 2: Determining the Change in Proton Number

Polonium-214 has an atomic number of 84 (which means it has 84 protons). During alpha decay, the nucleus loses 2 protons. Therefore, the product of this decay will have 84 - 2 = 82 protons.

Step 3: Writing the Nuclear Equation

The nuclear equation for the alpha decay of Polonium-214 can be written as follows:\[ \text{^{214}_{84}Po} \rightarrow \text{^{210}_{82}Pb} + \text{^{4}_{2}He} \]This shows that Polonium-214 decays into Lead-210 and an alpha particle.

Step 4: Identifying the Daughter Nucleus

The daughter nucleus resulting from the decay of Polonium-214 is Lead-210, as it has 82 protons, matching the atomic number of lead.

Key Concepts

Nuclear Equation

A nuclear equation is a symbolic representation of a nuclear reaction, similar to how a chemical equation represents a chemical reaction. It demonstrates the change that occurs in the nucleus of an atom during a nuclear process. In alpha decay, the equation effectively communicates how a parent nucleus transforms into a daughter nucleus by releasing an alpha particle.

In the process of alpha decay, an atom releases an alpha particle, composed of 2 protons and 2 neutrons. This results in a decrease in both atomic number and mass number for the original atom. Let's look at an example involving Polonium-214, which decays into Lead-210.

The nuclear equation for this process would be:

• Polonium-214: \( ext{^{214}_{84}Po} \)
• Alpha particle: \( ext{^{4}_{2}He} \)
• Lead-210 (Daughter Nucleus): \( ext{^{210}_{82}Pb} \)

The complete nuclear equation would then be: \[ ext{^{214}_{84}Po} \rightarrow \text{^{210}_{82}Pb} + \text{^{4}_{2}He} \]
This equation accurately depicts the transformation of Polonium to Lead due to the ejection of an alpha particle.

Radioactive Decay

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy by emitting radiation. Alpha decay is a common type of radioactive decay especially in heavy elements like Polonium. Understanding radioactive decay is crucial because it explains the mechanisms by which elements transform over time.

In alpha decay, the atom releases an alpha particle, which carries away 2 protons and 2 neutrons from the nucleus. This significantly alters the identity of the atom, reducing its atomic number by 2 and its mass number by 4. As a result, what was once a Polonium atom becomes a Lead atom due to a shift in its nuclear structure.

Key points to remember about radioactive decay:

• It releases particles or energy from the nucleus.
• Alpha particles consist of 2 protons and 2 neutrons.
• It changes elements by altering the number of protons and neutrons in the nucleus.

Understanding these shifts help scientists and students grasp how elements evolve and the implications for nuclear stability.

Daughter Nucleus

The daughter nucleus refers to the new isotope or element formed after a nuclear decay event, in this case, through alpha decay. It is the product that remains after the parent nucleus loses particles or energy. In alpha decay, the daughter nucleus has an atomic number two less than the original parent nucleus and a mass number four less.

To illustrate, let's consider the alpha decay of Polonium-214. The original nucleus, Polonium-214, loses 2 neutrons and 2 protons to become Lead-210, which is the daughter nucleus. This is shown in the nuclear equation:

• \( \text{^{214}_{84}Po} \rightarrow \text{^{210}_{82}Pb} \)
• Alpha particle: \( \text{^{4}_{2}He} \)

The daughter nucleus, Lead-210, retains the nucleons not expelled in the decay process.

Characteristics of the daughter nucleus include:

• It has a new identity (lead in this case) compared to the parent nucleus (polonium).
• It is usually more stable compared to its parent atom post-decay.
• It may itself be radioactive, continuing a decay chain until a stable nucleus is formed.

Understanding the daughter nucleus is important for mapping the transformation sequence of radioactive materials.