Question

You have just discovered a new radioactive element! You find that it first undergoes an alpha decay followed by a beta decay. During the alpha decay Q1 energy is released, and during the beta decay Q2 energy is released. Find an expression for the mass of the final product after these two decays in terms of the released energies, the mass of the parent nucleus, and the decay products. For your physical representation you should draw diagrams of the particles emitted in each decay with vectors representing their velocities and labels for their kinetic energy. Hint: you should use conservation of energy to find the expression.

Answer 1

Alpha Decay:

; for this reaction, energy release is given as,

Rearranging:

------- Equation 1

Beta Decay:

Similarly, as mentioned above, energy equation is as follows;

Rearranging:

------- Equation 2

Combining equation 1 and 2:

This is the derived expression for the mass of the final product.