Question

Write equations for the alpha decay of the following isotopes: a) 212 \(86 \mathrm{Rn}\) b) \({ }^{241} \mathrm{Am}\)

Short answer

Question: Write down the alpha decay equations for the given isotopes - 212 Rn (Radon-212) and 241 Am (Americium-241). Answer: The alpha decay equations for the given isotopes are: - For 212 Rn (Radon-212): $$^{212}_{86}\mathrm{Rn} \rightarrow ^{208}_{84}\mathrm{Po} + ^4_2\mathrm{He}$$ - For 241 Am (Americium-241): $$^{241}_{95}\mathrm{Am} \rightarrow ^{237}_{93}\mathrm{Np} + ^4_2\mathrm{He}$$

Step-by-step solution

Identify the starting isotope

We are given the isotope 212 Rn (Radon-212). Its mass number is 212, and its atomic number is 86.

Determine the alpha particle

An alpha particle is made up of two protons and two neutrons, so its mass number is 4, and its atomic number is 2 (since it has two protons). We can represent it as \({ }^{4}\mathrm{He}\) (Helium-4).

Write the alpha decay equation

The alpha decay equation can be written as: $$^{212}_{86}\mathrm{Rn} \rightarrow ^{A}_{Z}\mathrm{X} + ^4_2\mathrm{He}$$ Here, A and Z are the mass and atomic numbers of the resulting isotope (X).

Determine the resulting isotope

The resulting isotope will have a mass number A = 212 - 4 = 208, and an atomic number Z = 86 - 2 = 84. So, the alpha decay equation for 212 Rn (Radon-212) is: $$^{212}_{86}\mathrm{Rn} \rightarrow ^{208}_{84}\mathrm{Po} + ^4_2\mathrm{He}$$ For 241 Am (Americium-241):

Identify the starting isotope

We are given the isotope 241 Am (Americium-241). Its mass number is 241, and its atomic number is 95.

Determine the alpha particle

As before, an alpha particle is made up of two protons and two neutrons, so its mass number is 4, and its atomic number is 2. We can represent it as \({ }^{4}\mathrm{He}\) (Helium-4).

Write the alpha decay equation

The alpha decay equation can be written as: $$^{241}_{95}\mathrm{Am} \rightarrow ^{A}_{Z}\mathrm{X} + ^4_2\mathrm{He}$$ Here, A and Z are the mass and atomic numbers of the resulting isotope (X).

Determine the resulting isotope

The resulting isotope will have a mass number A = 241 - 4 = 237, and an atomic number Z = 95 - 2 = 93. So, the alpha decay equation for 241 Am (Americium-241) is: $$^{241}_{95}\mathrm{Am} \rightarrow ^{237}_{93}\mathrm{Np} + ^4_2\mathrm{He}$$

Key concepts

Radioactive Decay

Radioactive decay is a fundamental concept in nuclear physics where unstable atoms lose energy by emitting radiation. This process transmutes one element into another and can occur in several forms, including alpha decay, beta decay, and gamma radiation. Alpha decay specifically involves the release of an alpha particle, which is essentially a helium-4 nucleus consisting of two protons and two neutrons.

This type of decay happens because the original nucleus has too strong a nuclear force for its size, leading to instability. Over time, it naturally seeks stability by expelling particles and energy. The resultant atomic structure falls into a lower energy state and becomes a different element with a reduced mass number and atomic number, as demonstrated in the alpha decay equations provided in the textbook solutions.

Nuclear Physics

Nuclear physics is the branch of physics that studies the constituents and interactions of atomic nuclei. The most prominent forces within a nucleus are the strong nuclear force, which binds nucleons (protons and neutrons) together, and the electromotive force, which causes like-charged protons to repel each other.

Understanding nuclear physics is essential in explaining phenomena such as radioactive decay and nuclear fission or fusion reactions. The delicate balance of forces within a nucleus determines its stability and dictates which type of decay or nuclear reaction might occur. For instance, in alpha decay equations, the loss of an alpha particle is a consequence of adjustments within the nuclear binding energies and the overall pursuit of a more stable nuclear configuration.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons. This means that while they share the same atomic number, they have different mass numbers. For example, 212 Rn and 241 Am are isotopes of radon and americium, respectively.

These differences in neutron count lead to variations in the stability of the nucleus. Some isotopes are stable, while others, referred to as radioactive isotopes or radioisotopes, are prone to radioactive decay. The isotopes discussed in the alpha decay equations, such as Radon-212 and Americium-241, are examples of radioisotopes. Their decay helps to understand the natural transformation processes that elements undergo over time and their applications in fields like medicine, archaeology, and energy production.

Nucleon Number

The nucleon number, also known as the mass number, represents the total number of protons and neutrons in an atomic nucleus. Each nucleus is defined by two important numbers: the atomic number (number of protons) and the nucleon number. For instance, 212 Rn has 86 protons and 126 neutrons (86 + 126 = 212), confirming its nucleon number as 212.

In alpha decay, the nucleon number decreases by four due to the emission of two protons and two neutrons as part of the alpha particle. Similarly, the atomic number decreases by two as shown in the alpha decay equation for Radon-212. Understanding the nucleon number is crucial for writing and balancing nuclear equations, as it assists in predicting the identities of the resulting nuclides after the decay process.