Problem 20 - Chemistry The Molecular Science

Question

Radon-222 is unstable and its presence in homes may constitute a health hazard. It decays by this sequence of emissions: \(\alpha, \alpha, \beta, \beta, \alpha, \beta, \beta, \alpha .\) Write the sequence of nuclear reactions leading to the final product nucleus, which is stable.

Step-by-Step Solution

Answer

The stable nucleus is \( ^{206}_{82}\text{Pb} \).

Step 1: Determine Initial Nucleus

Radon-222 is denoted as \( ^{222}_{86}\text{Rn} \). This nucleus has an atomic number of 86 and a mass number of 222.

Step 2: Apply First Alpha Decay

An alpha particle \( ^{4}_{2}\text{He} \) is emitted, reducing both the atomic number and mass number. The new nucleus is \( ^{218}_{84}\text{Po} \).

Step 3: Apply Second Alpha Decay

Another alpha particle \( ^{4}_{2}\text{He} \) is emitted, resulting in \( ^{214}_{82}\text{Pb} \).

Step 4: Apply First Beta Decay

A beta decay emits an electron, converting a neutron into a proton. The new isotope is \( ^{214}_{83}\text{Bi} \).

Step 5: Apply Second Beta Decay

Another beta particle is emitted, transforming \( ^{214}_{83}\text{Bi} \) into \( ^{214}_{84}\text{Po} \).

Step 6: Apply Third Alpha Decay

Emitting another alpha particle results in \( ^{210}_{82}\text{Pb} \).

Step 7: Apply Third Beta Decay

A beta decay leads to the formation of \( ^{210}_{83}\text{Bi} \).

Step 8: Apply Fourth Beta Decay

Another beta particle emission results in \( ^{210}_{84}\text{Po} \).

Step 9: Apply Fourth Alpha Decay

A final alpha particle emission leads to the stable nucleus \( ^{206}_{82}\text{Pb} \).

Key Concepts

Alpha Decay

Alpha decay is a type of nuclear decay where an unstable nucleus releases an alpha particle to become more stable. It involves the emission of a particle composed of two protons and two neutrons, famously known as a helium nucleus, denoted as \(^4_2\text{He}\). When an alpha particle is emitted, the atomic number of the original element decreases by two and the mass number decreases by four. This is because the alpha particle takes with it two protons and two additional nucleons (neutrons). For example, in the decay of Radon-222 to Polonium-218, the equation is written as: \[^{222}_{86}\text{Rn} \rightarrow ^{218}_{84}\text{Po} + ^{4}_{2}\text{He}\]Alpha decay is quite common in heavier elements, those with a mass number higher than that of lead, as it helps the heavy nucleus to lose some mass, thus moving towards a more stable state.

Beta Decay

Beta decay is another form of nuclear decay, which involves the emission of beta particles. A beta particle is an electron or positron ejected from the nucleus when a neutron converts to a proton or vice versa. There are two types of beta decay: beta-minus and beta-plus.

• Beta-minus decay involves a neutron turning into a proton with the release of an electron and an antineutrino. This increases the atomic number by one without affecting the mass number since neutrinos have negligible mass.
• Beta-plus decay has a proton converting into a neutron, emitting a positron and a neutrino, lowering the atomic number by one.

In our original example, during the beta decay of Lead-214 to Bismuth-214, the transformation is shown as:\[^{214}_{82}\text{Pb} \rightarrow ^{214}_{83}\text{Bi} + \beta^-\]These changes allow unstable isotopes to adjust their proton-to-neutron ratio, often leading to more stable nuclei. Beta decay is more frequent among medium-weight isotopes.

Radon-222 Decay Series

The Radon-222 decay series is an important sequence of nuclear disintegrations in the natural radioactive decay chain. Starting off as Radon-222, a radioactive noble gas, it undergoes a series of alpha and beta decays until it eventually forms a stable isotope. Here's a brief overview of the sequence:

• Starts with Radon-222, the gas that poses health risks in homes.
• Consequent emissions include:
  • Two alpha decays to transform into Polonium-218
  • Two beta decays leading it to Bismuth-214
  • An alpha decay reaching Lead-210
  • Followed by two beta decays converging into Polonium-210
  • Finally, an alpha decay resulting in stable Lead-206

This decay sequence is crucial in understanding the pathways of radioactive decay as it involves multiple changes including emission of high-energy particles and radiations. Each step within this decay chain reduces the instability and radioactivity of the original element, ultimately ending with a non-radioactive, stable atom.