The radioisotope 226Ac can decay by any of three different nuclear processes: alpha emission, beta emission, or electron capture. (a) Write a balanced nuclear equation for the decay of 226Ac by each decay mode.

Verified step by step guidance

Step 1: Identify the initial isotope and its atomic number. The isotope given is 226Ac, which has an atomic number of 89 (Actinium).

Step 2: Write the nuclear equation for alpha emission. In alpha decay, the nucleus emits an alpha particle, which is a helium nucleus (\( ^4_2He \)). This reduces the mass number by 4 and the atomic number by 2.

Step 3: Write the nuclear equation for beta emission. In beta decay, a neutron is converted into a proton, and a beta particle (\( ^0_{-1}e \)) is emitted. This increases the atomic number by 1 while the mass number remains unchanged.

Step 4: Write the nuclear equation for electron capture. In electron capture, an inner orbital electron is captured by the nucleus, which combines with a proton to form a neutron. This decreases the atomic number by 1 while the mass number remains unchanged.

Step 5: Balance each nuclear equation by ensuring that the sum of the mass numbers and the sum of the atomic numbers are equal on both sides of the equation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Decay Processes

Nuclear decay processes are the mechanisms by which unstable atomic nuclei lose energy and particles to reach a more stable state. The primary types include alpha emission, where an alpha particle (two protons and two neutrons) is released; beta emission, where a neutron transforms into a proton and emits a beta particle (electron); and electron capture, where an electron is absorbed by a proton, converting it into a neutron.

Balanced Nuclear Equations

A balanced nuclear equation represents the transformation of an unstable nucleus into a more stable one, ensuring that the total number of protons and neutrons is conserved. In these equations, the sum of atomic numbers (protons) and mass numbers (protons + neutrons) must be equal on both sides of the equation, reflecting the conservation of mass and charge during the decay process.

Radioisotopes

Radioisotopes are isotopes of elements that are unstable and undergo radioactive decay, emitting radiation in the form of particles or electromagnetic waves. They are characterized by their half-lives, which indicate the time required for half of a sample to decay. Understanding the specific radioisotope, such as 226Ac, is crucial for predicting its decay modes and the resulting products of the decay process.

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