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Alpha decay is a type of nuclear decay where a nucleus emits an alpha particle. Essentially, an alpha particle is the same as a helium nucleus, represented by \( ^{4}_{2}\mathrm{He} \). These particles consist of two protons and two neutrons. As a result of this emission, both the atomic number \( Z \) and mass number \( A \) of the original atom change. Specifically, \( A \) decreases by 4, and \( Z \) drops by 2. This leads to the formation of a new element. For example, consider the decay of polonium-211 into lead-207. Here’s how it happens:

• Start with polonium-211: \( ^{211}_{84} \mathrm{Po} \)
• It emits an alpha particle \( ^{4}_{2}\mathrm{He} \)
• We end up with lead-207: \( ^{207}_{82} \mathrm{Pb} \)

Understanding this process helps in observing that during alpha decay, the parent nucleus changes into a different element, not just a lighter isotope of itself.

Beta decay is another kind of nuclear decay and comes in two main types: beta minus (\( \beta^{-} \)) and beta plus (\( \beta^{+} \)). Let's focus on beta minus decay, where a neutron in the nucleus turns into a proton. This change involves the emission of a beta particle, which is a high-speed electron (\( \beta^{-} \)), and an antineutrino symbolized by \( \overline{u} \). Here's what happens in beta minus decay:

• The mass number \( A \) of the nucleus remains constant.
• The atomic number \( Z \) increases by 1 because of the new proton.

To illustrate, look at the decay of thallium-207 to lead-207:

• We start with thallium-207: \( ^{207}_{81} \mathrm{Tl} \)
• It emits a beta particle and an antineutrino: \( \beta^{-} + \overline{u} \)
• We end up with lead-207: \( ^{207}_{82} \mathrm{Pb} \)

In beta decay, the nucleus doesn't change its mass, but it transforms into an isotope of the next element with a higher atomic number.

During nuclear decay processes, the nucleus formed after the decay is known as the daughter nucleus. This new nucleus is the "offspring" of the original nucleus or the parent nucleus. Whether through alpha or beta decay, the parent nucleus transitions to a daughter nucleus while emitting alpha or beta particles:

• In alpha decay, the daughter nucleus has a reduced atomic and mass number, leading to an entirely different element.
• In beta decay, the daughter nucleus typically becomes a more stable isotope of an adjacent element on the periodic table, due to the alteration in atomic number.

Using our examples: - For alpha decay of polonium-211, the daughter nucleus is lead-207. - For beta minus decay of thallium-207, the daughter nucleus is also lead-207. The daughter nucleus is always more stable than the parent, contributing to the natural progression towards stability in nuclear reactions.