Question

How much kinetic energy is released and what is the daughter nucleus in the \(\alpha\) decay of polonium \(-210 ?\)

Short answer

The daughter nucleus after the \(\alpha\) decay of Polonium-210 becomes Lead-206. The amount of kinetic energy released during the decay process depends on the mass and velocity of the alpha particle which requires addition data to estimate.

Step-by-step solution

Understanding Alpha Decay

In alpha decay, a nucleus releases an alpha particle which consists of two protons and two neutrons. So, the new nucleus has atomic number reduced by 2 units and nucleon number reduced by 4 units.

Identifying the Daughter Nucleus

Polonium (Po) has an atomic number of 84. Since an \(\alpha\) particle (which consists of 2 neutrons and 2 protons) is emitted, the atomic number of the resulting daughter nucleus will be \(84 - 2 = 82\), and the atomic mass will be \(210 - 4 = 206\). The nucleus with atomic number 82 is Lead (Pb). So, the daughter nucleus is Lead-206.

Determining The Energy Released

The energy released during alpha decay is the kinetic energy transferred to the alpha particle, given by the equation KE = 1/2 mv^2. We obtain the mass and velocity of the emitted alpha particle from respective atomic tables or decay energy references. The mass of an alpha particle is commonly given as \(4u\) where \(u\) is the atomic mass unit (\(1.66053906660 \times 10^{-27} kg\)). The velocity can be calculated by integrating the force over the distance it travels, which is often complex for nuclear physics and better to refer to alpha decay energy references. However, this exact calculation is not provided in the problem.

Key concepts

Kinetic Energy in Nuclear Decay

When an atomic nucleus decays by emitting an alpha particle, as in the case of polonium-210, it releases a specific amount of energy in the form of kinetic energy. The alpha particle, which is a helium-4 nucleus, carries away this energy as it zooms away from the parent nucleus. In physics, we know that the kinetic energy (KE) can be expressed with the equation \(KE = \frac{1}{2} mv^2\), where \(m\) is the mass and \(v\) is the velocity of the particle.

To understand this concept in the context of alpha decay, let's consider that the mass of an alpha particle is about 4 atomic mass units (amu), which can be converted into kilograms using the atomic mass unit factor \(1u = 1.66053906660 \times 10^{-27} kg\). Although the speed \(v\) of the alpha particle in polonium-210 decay is not specified, in actual practice it would typically be determined from experimental data or calculated from nuclear decay energy formulas. The released kinetic energy is a measure of the alpha particle's ability to do work, such as ionizing atoms or moving other particles, as it passes through matter.

Daughter Nucleus Identification

The identification of the daughter nucleus in a nuclear decay process is a key concept in understanding the aftermath of the decay. In the alpha decay of polonium-210, we can deduce the identity of the daughter nucleus by analysis of the decay event. As an alpha particle (consisting of two protons and two neutrons) is ejected, we compute the new atomic number by subtracting 2 from that of the parent nucleus, polonium, which has an atomic number of 84. This yields an atomic number of 82.

Similarly, the nucleon number, which includes both protons and neutrons in the nucleus and is also referred to as the mass number, decreases by 4. Hence, the nucleon number for polonium-210 becomes 206 after the alpha decay. These numbers, atomic number 82 and mass number 206, correspond to the element lead (Pb). Hence, the daughter nucleus formed is Lead-206. By recognizing these changes, students can effectively identify the products of nuclear decay processes.

Atomic Number Reduction

In nuclear reactions, such as alpha decay, the atomic number of a nucleus represents the number of protons it contains. The atomic number is crucial because it defines the element to which the atom belongs. During alpha decay, the atomic number reduces because an alpha particle contains 2 protons, and its emission means the original nucleus loses those 2 protons.

This decrement results in a formation of a different element altogether. For example, in the alpha decay of polonium-210, the atomic number decreases from 84 to 82. As a consequence of losing two protons, polonium transforms into lead. Students need to grasp this concept to understand how certain elements can change into others via radioactive decay processes.

Nucleon Number Decrease

The nucleon number, also known as the mass number, is the sum of protons and neutrons in an atom's nucleus. In the context of alpha decay, when a parent nucleus emits an alpha particle, this number is reduced by 4 because an alpha particle consists of 2 protons and 2 neutrons. Since the nucleon number is conserved in nuclear processes, the particles’ nucleon numbers before and after the decay should be equal.

In our example of polonium-210 undergoing alpha decay, the nucleon number decreases from 210 to 206. This reduction parallels the creation of a lighter nucleus, lead-206, from the heavier polonium-210. Understanding the concept of nucleon number is fundamental for students to comprehend the mass changes in nuclear reactions and to balance nuclear equations accordingly.