We’re being asked to write a **nuclear equation for the most likely mode of decay of Th-221**.

We will do the following steps to solve this problem:

Step 1: Determine the mode of decay

Step 2: Write the nuclear equation

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}_{–1}**β)** or neutron emission (^{1}_{0}n; not in the choices)

• **below** the valley of stability: there **too many protons** in the isotope

Mode of decay: Either **positron emission (**^{0}_{1}**e)** or **electron capture (**^{0}_{–1}**e)**

• with **atomic mass ≥ 200 amu**: there **too many protons and neutrons** in the isotope

Mode of decay: **alpha decay (**^{4}_{2}**α)**

Write a nuclear equation for the most likely mode of decay for each of the following unstable nuclides.

Th-221

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.