20150624

Physics final exam question: Cu-64 decay processes and daughter isotopes

Physics 205B Final Exam, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 29.4, Problem 29.26

Cu(64,29) can either undergo either β decay or electron capture. Discuss whether these two processes will both result in the same daughter isotope, or instead will result in two different types of daughter isotopes. Explain your reasoning using properties of nuclides and radioactive decay modes.

Solution and grading rubric:
  • p:
    Correct. Compares the two decay processes:
    1. β- decay emits an electron, in the process converting a neutron into a proton, which leaves the nucleon number the same, but increases the atomic number (resulting in zinc);
    2. electron capture takes in an electron to covert a proton into a neutron, which also leaves the nucleon number the same, but decreases the atomic number (resulting in nickel); thus two different types of daughter elements (different proton numbers) result from these two decay processes. (The daughter elements need not be explicitly named, as long as the different proton numbers are recognized.)
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying properties of radioactive decay.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying properties of radioactive decay.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: finalLd0c
p: 16 students
r: 6 students
t: 5 students
v: 8 students
x: 2 students
y: 2 students
z: 4 students

A sample "p" response (from student 0104):

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