Question

Write a balanced nuclear equation for the alpha decay of each of the following radioactive isotopes: a. curium- 243 b. \({ }_{99}^{252} \mathrm{Es}\) c. \({ }_{98}^{251} \mathrm{Cf}\) d. \({ }_{107}^{261} \mathrm{Bh}\)

Short answer

a. \(_{96}^{243} \text{Cm} \to _{94}^{239} \text{Pu} + _{2}^{4} \text{He}\); b. \(_{99}^{252} \text{Es} \to _{97}^{248} \text{Bk} + _{2}^{4} \text{He}\); c. \(_{98}^{251} \text{Cf} \to _{96}^{247} \text{Cm} + _{2}^{4} \text{He}\); d. \(_{107}^{261} \text{Bh} \to _{105}^{257} \text{Db} + _{2}^{4} \text{He}\)\).

Step-by-step solution

Understanding Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle consists of 2 protons and 2 neutrons, which is a helium-4 nucleus \((_{2}^{4} \text{He})\). This decay decreases the mass number by 4 and the atomic number by 2.

Balancing Curium-243 Alpha Decay

The isotope curium-243 \((_{96}^{243} \text{Cm})\) undergoes alpha decay. This will yield a new nucleus with 2 fewer protons and 4 fewer mass units compared to curium-243. So, \(_{96}^{243} \text{Cm} \to _{94}^{239} \text{Pu} + _{2}^{4} \text{He}\).

Balancing Einsteinium-252 Alpha Decay

For the isotope \({ }_{99}^{252} \text{Es}\), the alpha decay results in the emission of an alpha particle, reducing the atomic number by 2 and the mass number by 4. Thus, \(_{99}^{252} \text{Es} \to _{97}^{248} \text{Bk} + _{2}^{4} \text{He}\).

Balancing Californium-251 Alpha Decay

The isotope \({ }_{98}^{251} \text{Cf}\) undergoes alpha decay by losing an alpha particle, leading to: \(_{98}^{251} \text{Cf} \to _{96}^{247} \text{Cm} + _{2}^{4} \text{He}\).

Balancing Bohrium-261 Alpha Decay

For \({ }_{107}^{261} \text{Bh}\), after alpha decay, the atomic number decreases by 2 and the mass number decreases by 4. Therefore, the equation is: \(_{107}^{261} \text{Bh} \to _{105}^{257} \text{Db} + _{2}^{4} \text{He}\).

Key concepts

radioactive decay

Radioactive decay is a process in which an unstable atomic nucleus loses energy by emitting radiation. This helps the nucleus to achieve a more stable state. There are different types of radioactive decay mechanisms such as alpha decay, beta decay, and gamma decay. In alpha decay, an alpha particle, which consists of 2 protons and 2 neutrons (equivalent to a helium-4 nucleus), is emitted from the decaying nucleus. This emission reduces the mass number by 4 and the atomic number by 2.

Understanding radioactive decay is crucial for studying nuclear reactions and natural radioactivity. By analyzing decay processes, scientists can better understand the properties of matter and the forces at play inside atomic nuclei. Alpha decay, specifically, is an important concept in both physics and chemistry for explaining how heavy elements transform into lighter elements over time.

nuclear equations

Nuclear equations are symbolic representations of nuclear reactions. They illustrate how the atomic nuclei of elements change during various nuclear processes. In these equations, we use atomic symbols to denote the elements and superscripts/subscripts to indicate the mass number (total protons and neutrons) and the atomic number (total protons) respectively. For instance, in the equation for curium-243's alpha decay: \(_{96}^{243} \text{Cm} \to _{94}^{239} \text{Pu} + _{2}^{4} \text{He}\).The left side represents the original radioactive isotope, and the right side shows the products of the decay—in this case, a plutonium nucleus and an alpha particle.

When writing nuclear equations, it’s essential to ensure that both the mass numbers and the atomic numbers are balanced on both sides of the equation. This reflects the conservation laws we observe in nuclear processes. Writing and balancing nuclear equations help us understand the specific changes occurring in the nuclei during nuclear reactions.

balancing chemical equations

Balancing chemical equations is a fundamental skill in chemistry and nuclear physics. It ensures that the same number of atoms of each element are present on both sides of a reaction equation. Since atomic nuclei are involved, nuclear equations must also be balanced in terms of both mass number and atomic number. This conservation is rooted in the principle that matter cannot be created or destroyed, only transformed.

To balance a nuclear equation, follow these steps:

• Identify the initial nucleus (reactant) and the resulting nuclei (products).
• Calculate the total number of protons and neutrons on both sides of the equation.
• Adjust coefficients if necessary to make sure both sides have equal mass numbers and atomic numbers.

For alpha decay specifically, the emitted alpha particle always has a mass number of 4 and an atomic number of 2. As such, alpha decay reduces the original nucleus’s mass number by 4 and its atomic number by 2.

For example, when balancing the alpha decay of curium-243: \(_{96}^{243} \text{Cm} \to _{94}^{239} \text{Pu} + _{2}^{4} \text{He}\) We see that the sum of mass numbers ( \(243 = 239 + 4\)) and atomic numbers ( \(96 = 94 + 2\)) are identical on both sides.

isotopes

Isotopes are different forms of the same element, having the same number of protons (atomic number) but different numbers of neutrons, leading to different mass numbers. For example, curium has several isotopes, including curium-243 and curium-244. Each isotope of an element exhibits nearly identical chemical behavior but may have different nuclear properties, such as stability and radioactive decay characteristics.

The term 'isotope' highlights the diversity of atomic nuclei that an element can have. In nuclear reactions, understanding the specific isotope involved is crucial as different isotopes can undergo different types of decay, at varying rates. For instance:

• Curium-243 can decay via alpha emission to become plutonium-239.
• Similarly, californium-251 emits an alpha particle to form curium-247.

These transformations show how isotopes of heavy elements break down into lighter elements, helping scientists track changes in atomic structures and predict behaviors of substances.