Question

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

Short answer

The stable nucleus formed after the decay of Radon-222 consisting of three alpha emissions and two beta emissions is Lead-210 (\(^{210}_{82}Pb\)).

Step-by-step solution

Recall alpha and beta decay process

Before solving this exercise, it is necessary to recall the particle emissions in alpha and beta decays: 1. In alpha decay, an alpha particle (which is a Helium-4 nucleus, containing 2 protons and 2 neutrons) is emitted. This leads to the atomic number decreasing by 2 and the mass number decreasing by 4. 2. In beta decay, a beta particle (a high-energy electron) is emitted. This occurs when a neutron changes into a proton and an electron, causing the atomic number to increase by 1, while the mass number remains unchanged.

Write the initial Radon-222 isotope

Radon-222 has an atomic number of 86 and a mass number of 222. We represent the isotope as \(^{222}_{86}Rn\).

Perform the first alpha decay

In the first alpha decay, the atomic number decreases by 2 and the mass number decreases by 4. New isotope: \(^{218}_{84}Po\) (Polonium-218)

Perform the second alpha decay

In the second alpha decay, the atomic number decreases by 2 again and the mass number decreases by 4. New isotope: \(^{214}_{82}Pb\) (Lead-214)

Perform the third alpha decay

In the third alpha decay, the atomic number decreases by 2 and the mass number decreases by 4. New isotope: \(^{210}_{80}Hg\) (Mercury-210)

Perform the first beta decay

In the first beta decay, the atomic number increases by 1, and the mass number remains unchanged. New isotope: \(^{210}_{81}Tl\) (Thallium-210)

Perform the second beta decay

In the second beta decay, the atomic number increases by 1, and the mass number remains the same as in the previous step. New isotope: \(^{210}_{82}Pb\) (Lead-210) So, the stable nucleus formed after the decay of Radon-222 consisting of three alpha emissions and two beta emissions is Lead-210.

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle is essentially a Helium-4 nucleus with two protons and two neutrons. This emission results in a significant decrease in both the atomic number and the mass number of the original element. In the case of Radon-222, during alpha decay, Radon emits an alpha particle, reducing its atomic number by 2 and its mass number by 4. Such a change transforms it into a different element, Polonium-218. This type of decay continues, changing the element each time until a stable one is formed. Some common characteristics of alpha decay include:

• Decrease in atomic number by 2
• Decrease in mass number by 4
• Formation of a new element each time an alpha particle is emitted

Alpha decay generally occurs in heavier elements that need to release mass to attain a more stable state, often resulting in the formation of entirely new elements with lower atomic numbers.

Beta Decay

Beta decay is a different form of radioactive decay where a neutron in the nucleus transforms into a proton and an electron. This electron is known as a beta particle and is ejected from the nucleus. Unlike alpha decay, beta decay only affects the atomic number of the element, while leaving the mass number unchanged. In Radon-222’s transformation, after several alpha decays, beta decay comes into play. The emission of a beta particle increases the atomic number by 1, essentially converting one element to the next in the periodic table. For instance, through this process, Mercury-210 is transformed into Thallium-210, raising the atomic number while keeping the mass the same. Key points about beta decay:

• Increase in atomic number by 1
• Mass number remains the same
• Transformation of neutron into proton thereby changing the element

Beta decay allows an atom to move closer to a stable neutron to proton ratio, finding a more stable nuclear configuration.

Nuclear Chemistry

Nuclear chemistry focuses on reactions and changes occurring in the nucleus of an atom. It explores radioactive decay processes, nuclear fission, and fusion, helping us understand the forces and reactions that stabilize or destabilize atomic nuclei. Radon-222’s journey through multiple decays to stabilize as Lead-210 provides a clear example of how nuclear chemistry operates. In fact, each emission (alpha or beta) is a nuclear reaction triggered by the natural instability of an isotope. Nuclear chemistry covers:

• Exploration of radioactive decay types like alpha and beta decay
• Analysis of fission and fusion processes
• Understanding how energy is conserved during nuclear transformations

By studying nuclear chemistry, we gain deeper insights into the fundamental processes that govern the universe’s composition, enabling us to harness nuclear reactions for practical uses like energy production and medical treatments.

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons. This means isotopes of the same element have the same atomic number but different mass numbers. Radon-222 is an isotope of Radon, characterized by its specific number of protons and neutrons. As it undergoes decay, it is transformed into other isotopes and eventually reaches a stable state as Lead-210. Each isotope along the way has unique properties, influencing how it behaves during decay. Key characteristics of isotopes:

• Same number of protons, different number of neutrons
• Have different mass numbers
• May exhibit different stability and reactivity

Understanding the concept of isotopes is essential in nuclear chemistry as it helps foresee an element’s decay pattern and stability, ultimately impacting how we utilize and manage radioactive substances in various fields like medicine and energy.