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Alpha decay is a fundamental type of radioactive decay. In this process, an unstable atomic nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, which makes it identical to a helium-4 nucleus, represented as \(_2^4He\) or \(^4_2He\). As a result, the original atom loses 4 units from its mass number and 2 units from its atomic number.
For instance, when curium-243 (represented as \(_{96}^{243}Cm\)) undergoes alpha decay, it loses an alpha particle and turns into plutonium-239 (represented as \(_{94}^{239}Pu\)). We write this nuclear transformation as follows:
\[{}_{96}^{243}Cm \rightarrow {}_{94}^{239}Pu + {}_{2}^{4}He\]
This balanced equation shows the transformation clearly: Curium loses an alpha particle and converts into Plutonium.

A balanced nuclear equation is crucial in understanding nuclear reactions. It must satisfy both the conservation of mass and the conservation of charge. This means the total number of protons and neutrons (mass number) and the total electrical charge (atomic number) must be the same on both sides of the equation.
Let's take the example of \({ }^{252}Es\):
\[{}_{99}^{252}Es \rightarrow {}_{97}^{248}Bk + {}_{2}^{4}He\]
In this equation:

• The total mass number on the left is 252, and it matches the sum 248 (from Bk) + 4 (from He) on the right side.
• The total atomic number on the left is 99, and it matches the sum 97 (from Bk) + 2 (from He) on the right side.

Thus, the nuclear equation is balanced.

Radioactive isotopes are variants of elements that have unstable nuclei. These isotopes tend to emit radiation as they decay into more stable forms. Radionuclides such as curium-243, \({ }^{252}Es\), and others mentioned in the exercise are examples of such isotopes.
These isotopes undergo decay because their nucleus contains excess energy or an unusual number of neutrons compared to protons. During the decay process, the isotope transforms into a different element entirely. For example, curium-243 transforms into plutonium-239, while Bohrium-261 decays to produce Dubnium-257.
Their applications in various fields, including medicine and energy, make understanding their decay essential. In nuclear reactors, for instance, these decays produce the energy required for electricity generation.

Nuclear reactions involve changes in an atom's nucleus, leading to the conversion of elements. These reactions differ from chemical reactions, which involve only electrons in atoms. There are several types of nuclear reactions, including alpha decay, beta decay, and fission.
In alpha decay, a heavy nucleus emits an alpha particle to become a different element. Each reaction adheres to strict conservation laws, preserving the number of nucleons (protons + neutrons). For example, when californium-251 undergoes alpha decay:
\[{}_{98}^{251}Cf \rightarrow {}_{96}^{247}Cm + {}_{2}^{4}He\]
Once again, the mass numbers and atomic numbers are balanced across both sides. The practical uses of these reactions are vast, from generating nuclear power to understanding cosmic phenomena.
Understanding alpha decay equips students to better appreciate both the science behind these reactions and their broader implications in the world.