We’re being asked to predict the most likely mode of decay for each of the radioactive isotope given.
Recall that the stability of an isotope depends on the ratio of neutrons to protons (N/Z). This means for stable isotopes with:
• Z ≤ 20; the N/Z ratio should be equal to 1.0
• 20 < Z ≤ 40; the N/Z ratio should be equal to 1.25
• 40 < Z ≤ 80; the N/Z ratio should be equal to 1.50
• Z < 83; the stable nuclide does not exist
The N/Z values for stable isotopes form the valley or band of stability:
This means for isotopes:
• above the valley of stability: there too many neutrons in the isotope
Mode of decay: Either beta decay (0–1β) or neutron emission (10n; not in the choices)
• below the valley of stability: there too many protons in the isotope
Mode of decay: Either positron emission (01e) or electron capture (0–1e)
• with atomic mass ≥ 200 amu: there too many protons and neutrons in the isotope
Mode of decay: alpha decay (42α)
Recall that the atomic mass is the sum of protons and neutrons and the atomic number tells us the number of protons.
Which type of nuclear decay is the following radioactive isotope likely to undergo?
a) beta decay
b) alpha decay
c) positron emission or electron capture
All known stable isotopes are shown on the graph. The points form what is know as the "belt of stability".
If a radioactive isotope is above the belt of stability, think about what type of decay would decrease its N/Z ratio. If an unstable isotope is below the belt of stability, think about what type of decay would increase its N/Z ratio. If a radioactive isotope is off the chart (Z > 83), think about what type of decay would decrease Z the most.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Band of Stability concept. You can view video lessons to learn Band of Stability. Or if you need more Band of Stability practice, you can also practice Band of Stability practice problems.