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)
There are four stable isotopes of iron with mass numbers 54, 56, 57, and 58. There are also two radioactive isotopes: iron-53 and iron-59. Predict modes of decay for these two isotopes. (See in the following table.)
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