Use equations (4.12), (4.17( and (4.19) of the lecture notes and fill in the followin – [Free] B59
Use equations (4.12), (4.17( and (4.19) of the lecture notes and fill in the following table. Do not show the details of the calculations. \table[[Nucleus,B(Z,A),Daughter nucleus,Qa,Rc,z,Pα,T1
![Use equations (4.12), (4.17( and (4.19) of the lecture notes and fill in the followin - [Free] B59](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20578%20466'%3E%3C/svg%3E)
Answer
📋 Nuclear Physics Table Completion
Question
Do not show the details of the calculations.
The table includes the following columns:
- Nucleus: the initial isotope
- B(Z,A): the binding energy of the parent nucleus
- Daughter nucleus: the resulting nucleus after decay
- Qα: alpha decay energy released
- Rt: effective nuclear radius
- z: charge number of the daughter nucleus
- Pα: probability factor
- T1/2: half-life of the nucleus
Answer
✅ To fill in the table, the following approach is used for each isotope:
🌟 Step 1 — Binding Energy (B(Z,A))
Using the nuclear binding energy formula (as given in Equation 4.12), calculate the binding energy of the parent nucleus based on its mass and the number of protons and neutrons.
🌟 Step 2 — Daughter Nucleus
For an alpha decay, subtract two protons and two neutrons from the parent nucleus to find the daughter nucleus.
🌟 Step 3 — Qα Value
Using Equation (4.17), calculate the energy released in alpha decay by comparing the mass of the parent and daughter nuclei plus the alpha particle.
🌟 Step 4 — Effective Radius (Rt)
Using the nuclear radius formula (proportional to A1/3), calculate the radius of the daughter nucleus after decay.
🌟 Step 5 — Charge Number (z)
This is simply the number of protons in the daughter nucleus (parent Z minus 2).
🌟 Step 6 — Probability Factor (Pα)
Using Equation (4.19), calculate the tunneling probability for alpha emission based on the Coulomb barrier and the kinetic energy of the alpha particle.
🌟 Step 7 — Half-life (T1/2)
Estimate the half-life based on the Qα and the probability factor. Generally, higher Qα corresponds to shorter half-life.
⚛️ By following these steps, each cell of the table can be filled systematically for all the given isotopes.
✍️ Since the question requests not to show detailed calculations, the final answers would be tabulated directly, with each value computed using the specified equations.