Answer Happy

a. (0.5 pts) Determine the Q-value and half-life for 238U alpha
decaying to 234Th, by looking it up on NNDC or the Colourful
Nuclear Chart b. (0.5 pt) Estimate the inner radius, a, in fm using
the relation 𝑅 = 𝑟0𝐴 1/3 , 𝑟0 = 1.2 fm, assuming that prior to
decay the 234U and 𝛼 particles are touching. c. (1 pt) What is the
frequency 𝑓 (in s-1 ) of the alpha particle hitting the potential
barrier at a? d. (1 pt) Using the expression in the slides,
determine 𝑏, the outer radius of the potential experienced by the 𝛼
in fm. Is it ok to use the approximation that the barrier is thick?
e. (2 pt) Using the expression for the Gamow factor from the
slides, determine the tunneling probability T f. (2 pt) Hence, find
the expected half-life for 238U decaying into 234Th. How does it
compare to the value found in part (a)? Why might it be
different?
Tunneling model of alpha emission V(a) 1) (7 pts). Here, we're going to calculate the half-life for 238 U decay using the preformed a decay theory we discussed in class that considers a Coulomb potential of the form shown on the left. a. (0.5 pts) Determine the Q-value and half-life for 238 U alpha decaying to 234Th, by looking it up on NNDC or the Colourful Nuclear Chart r b. (0.5 pt) Estimate the inner radius, a, in fm using the relation R = ro 4¹/3, To = 1.2 fm, assuming that prior to decay the 234U and a particles are touching. Separation of centers (fermis) c. (1 pt) What is the frequency f (in s¹) of the alpha particle hitting the potential barrier at a? d. (1 pt) Using the expression in the slides, determine b, the outer radius of the potential experienced by the a in fm. Is it ok to use the approximation that the barrier is thick? e. (2 pt) Using the expression for the Gamow factor from the slides, determine the tunneling probability T f. (2 pt) Hence, find the expected half-life for 238 U decaying into 234Th. How does it compare to the value found in part (a)? Why might it be different? 30 8 Energy (MeV) 00