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

1. Step 1: Identify the initial isotope and its atomic number. The isotope given is 226Ac, which has an atomic number of 89 (Actinium).
2. 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.
3. 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.
4. 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.
5. 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.