20170602

Physics final exam question: β+ decay of oxygen isotopes

Physics 205B Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

Unstable oxygen isotopes O(15,8) and O(19,8) can undergo some type of beta decay to become more stable[*]. Determine which one of these two isotopes (or both, or neither) will specifically undergo β+ decay. Explain your reasoning using the properties of nuclides and radioactive decay modes.

[*] wki.pe/Isotopes_of_oxygen.

Solution and grading rubric:
  • p:
    Correct. Recognizes that O(15,8) would undergo β+ decay, but not O(19,8) by discussing:
    1. a stable nucleus has a number of neutrons that are equal to or slightly greater than the number of protons; and
    2. β+ decay converts a proton to a neutron (by emitting a positron and a neutrino), decreasing the number of protons and increasing the number of neutrons in the nucleus; such that
    3. O(15,8) (which has seven neutrons and eight protons) undergoing β+ decay results in N(15,7) with a more favorable ratio of eight neutrons to seven protons), so β+ decay is possible for this oxygen isotope; while
    4. O(19,8) (which has 11 neutrons and eight protons) undergoing β+ decay results in N(19,7), which is a less favorable ratio of 12 neutrons to seven protons), so β+ decay is not likely for this oxygen isotope.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have only discussed why O(15,8) would undergo β+ decay, but does not discuss why O(19,8) would not.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. At least understands β+ decay (and other weak interaction decays), but does not properly discuss how ratio of neutrons to protons affects stability.
  • 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 nuclides and radioactive decay modes.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of nuclides and radioactive decay modes.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 11 students
r: 5 students
t: 3 students
v: 3 students
x: 3 students
y: 0 students
z: 1 student

A sample "p" response (from student 3575):

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