Chemistry Practice Problems Band of Stability Practice Problems Solution: Using general tendencies, predict the most likely ...

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Solution: Using general tendencies, predict the most likely mode of decay of each of the following radioactive isotopes.( α decay , β decay, e emission, e capture)1. iodine-1372. sodium - 203. thorium- 2324. mercury- 1905. potassium- 47

Problem

Using general tendencies, predict the most likely mode of decay of each of the following radioactive isotopes.

( α decay , β decay, e emission, e capture)

1. iodine-137

2. sodium - 20

3. thorium- 232

4. mercury- 190

5. potassium- 47

Solution

We’re being asked to predict the most likely mode of decay for each of the following radioactive isotopes


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)


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