Write a nuclear equation for the indicated decay of each nuclide. MISSED THIS? a. U-234 (alpha) b. Th- 230 (alpha) c. \(\mathrm{Pb}-214\) (beta) d. \(\mathrm{N}-13\) (positron emission) e. Cr-51 (electron capture)

Alpha decay is a common mode of radioactive decay where an unstable atomic nucleus emits an alpha particle and transforms into a lighter nucleus. An alpha particle is essentially a helium-4 nucleus, meaning it contains 2 protons and 2 neutrons.

For instance, in the decay of Uranium-234 (U-234), the emission of an alpha particle results in Thorium-230 (Th-230). Mathematically, this is represented as:
\[\mathrm{^{234}_{92}U \rightarrow ^{230}_{90}Th + ^{4}_{2}He}\]
As seen in this reaction, the atomic number decreases by 2 and the mass number by 4. Understanding this principle helps to accurately predict the resulting isotopes after alpha decay.

Beta decay is another type of radioactive decay where a nucleus emits a beta particle. A beta particle can be either an electron or a positron, but when we refer to 'beta decay', we often mean the emission of an electron. Here, a neutron is transformed into a proton, which increases the atomic number of the nucleus by 1 while the mass number remains unchanged.

For example, when Lead-214 (Pb-214) undergoes beta decay, it emits an electron and becomes Bismuth-214 (Bi-214):
\[\mathrm{^{214}_{82}Pb \rightarrow ^{214}_{83}Bi + e^{-}}\]
This process is vital for balancing the neutron-to-proton ratio in atomic nuclei and is pivotal in the transformation of one element to another within the periodic table.

Positron emission, also known as positive beta decay, occurs when a proton in the nucleus is converted into a neutron and a positron is emitted along with a neutrino. The emission of the positron effectively decreases the atomic number by 1, but the mass number does not change.

For example, when Nitrogen-13 (N-13) undergoes positron emission, it yields Carbon-13 (C-13):
\[\mathrm{^{13}_{7}N \rightarrow ^{13}_{6}C + e^{+}}\]
Such types of decay are important to understand in nuclear chemistry and in various applications, such as medical imaging techniques like positron emission tomography (PET).

Electron capture is a process where an inner orbital electron is absorbed by the nucleus, which combines with a proton to produce a neutron and typically a neutrino. It's a less familiar form of decay but equally significant as it decreases the atomic number by 1 with no change to the mass number.

Chromium-51 (Cr-51) transforming into Vanadium-51 (V-51) can serve as an example:
\[\mathrm{^{51}_{24}Cr + e^{-} \rightarrow ^{51}_{23}V + u}\]
Understanding electron capture is not only crucial for nuclear physics but also for studying the sun and neutrino physics, where this phenomenon naturally occurs.

Radioactive decay is the spontaneous transformation of one chemical element or isotope into another. This process occurs as unstable atomic nuclei release energy in the form of radiation, transforming into more stable forms. There are many types of radioactive decay, including alpha, beta, and gamma decay, as well as other less common types such as positron emission and electron capture discussed above.

Each type of decay affects both the atomic and mass numbers of the resulting atoms in characteristic ways. It's a natural process that allows us to date ancient artifacts through techniques like carbon dating, provides energy through nuclear power, and can be used for treatment in medicine with radiotherapy. Learning how to write nuclear decay equations, such as those for U-234 or Pb-214, provides a window into the stability and transmutation of elements in the universe.