Answer Happy

(2.5 points total) In an assignment you showed that the alpha decay rate is la = fP = f exp -Zpe2 4e Zpma 1/27 + Eohv ħ πέο = = () ] where a is the sum of the radii of the alpha particle and the daughter nucleus, Zą and Zp are their respective charges, m is their reduced mass, f is the assault frequency, and P is the probability of transmition through the Coulomb barrier. (a) (1 point) Writing v in terms of the Q-value of the reaction deduce the Geiger- Nutall law C2 log T = (1+ ✓ where T is the half-life. What are ci and ca? (b) (0.5 points) Assuming that f v/a, calculate the assault frequency and the decay rate, using your results above, for the alpha emission of 212 Ra. Compare your results with the value found in the nuclear data base. (c) (1 point) Consulting the nuclear data base, consider other 4 isotopes of Radium that undergo alpha decay (your choice). Draw the experimental values of the half-lives against 1/Q in a logarithmic scale. Find a fit for the data. What is your conclusion about the accuracy of the Geiger-Nutall law?