I am having trouble understanding what the concept is for writing these out. Write a balanced nuclear equation for the alpha decay of each of the following radioactive isotopes: curium-243, 22589Ac

It's really quite simple to balance them. First, because the computer doesn't write subscripts and superscripts as we wish, this is my format. The first number is the atomic number. That is followed by the symbol of the element and that is followed by the mass number. 27Co60 is Co, atomic mass 27 and mass number 60. The secret to these equations is to make the atomic numbers balance on both sides and to make the mass numbers balance on both sides. The alpha particle is 2He4.

96Cm243 ==> 2He4 + yXz
So 96 = 2+y; therefore, y must be 94
Element #94 = Pu
243 = 4+z; therefore, z must be 239 and the full equation is
96Cm243 = 2He4 + 94Pu239

To write a balanced nuclear equation for alpha decay, you need to understand the basic principles of radioactive decay. Alpha decay occurs when a radioactive nucleus emits an alpha particle, which consists of two protons and two neutrons.

To write the balanced nuclear equation for alpha decay, follow these steps:

1. Identify the parent isotope: In the given examples, the parent isotopes are curium-243 (Cm-243) and actinium-225 (Ac-225).

2. Determine the daughter isotope: In alpha decay, the emission of an alpha particle reduces the atomic number by 2 (since the alpha particle carries two protons) and the mass number by 4 (since it carries two protons and two neutrons). The daughter isotope is the parent isotope with decreased atomic and mass numbers.

3. Write the equation: Start by writing the parent isotope on the left side of the equation, and then write the alpha particle as He-4 on the right side. Add a plus sign to separate the two sides.

- For the alpha decay of curium-243 (Cm-243):
Cm-243 -> He-4 + ?

- For the alpha decay of actinium-225 (Ac-225):
Ac-225 -> He-4 + ?

4. Determine the daughter isotope: To find the daughter isotope, subtract 2 from the atomic number (since an alpha particle carries two protons) and subtract 4 from the mass number (since an alpha particle carries two protons and two neutrons).

- For Cm-243 -> He-4 + X, the daughter isotope is americium-239 (Am-239).

- For Ac-225 -> He-4 + X, the daughter isotope is thorium-221 (Th-221).

5. Write the final balanced equation: Add the daughter isotope to the equation.

- For the alpha decay of curium-243 (Cm-243):
Cm-243 -> He-4 + Am-239

- For the alpha decay of actinium-225 (Ac-225):
Ac-225 -> He-4 + Th-221

That's how you write the balanced nuclear equations for alpha decay. Remember, these equations are balanced in terms of both mass numbers and atomic numbers.