Alex and Casey are analyzing a sample of asteroid material from Bennu, brought back by the OSIRIS-REx mission. They are using their knowledge of radioactive decay to identify the elements in the sample and determine its age.

1. Alex and Casey discovered a new radioactive element in the Bennu sample. How would they determine the type of radiation it emits (alpha, beta, or gamma)?
2. Alex suggests using alpha decay to identify the elements in the Bennu sample.
   1. How would you explain alpha decay to Casey and why it might be useful?
   2. During their research, Casey finds that the kinetic energy of an emitted alpha particle is 5 MeV. If the mass of the alpha particle is 4 amu, what is its velocity (using 1 amu = 1.66 10 kg and 1 MeV = 1.6 10 J)?
3. While studying the substructure of the nucleus, Alex and Casey identify an unusual nuclear configuration. How can they determine if the configuration is stable or prone to decay?
4. During their analysis, Alex and Casey discover traces of uranium in the sample. How would you explain the significance of finding uranium in an asteroid?
5. Casey measures the initial activity of their sample as 600 disintegrations per minute (dpm).
   1. What is the initial activity of the sample in Becquerels (Bq)?
   2. Casey discovers a sample with a decay constant of 0.0693 per hour. What is the half-life of this sample?
   3. If the half-life is 10 hours, what will be the activity (in Bq) after 30 hours?

6. Casey observes that a certain isotope in the Bennu sample undergoes beta decay. How do the conservation laws of energy and momentum apply to this process?

7. Casey wants to calculate the binding energy of a nucleus they found in the Bennu sample. a. What information do they need and what formula should they use? b. Casey finds the mass of the radioactive nucleus to be less than the combined mass of its constituent protons and neutrons. If the mass defect (m) is 0.1 atomic mass units (amu), what is the binding energy of the nucleus in MeV (using 1 amu = 931 MeV)?

8. Alex is curious about the role of quantum tunneling in the radioactive decay of the Bennu sample. How would you explain this phenomenon?