Question

If a nucleus of \({ }_{90}^{232} \mathrm{Th}\) absorbs a neutron and the resulting nucleus undergoes two successive beta decays, which nucleus results?

Short answer

The resulting nucleus is uranium-233 ( { }_{92}^{233} ext{U} ).

Step-by-step solution

Understand Neutron Absorption

When the thorium-232 ( { }_{90}^{232} ext{Th} ) nucleus absorbs a neutron, it becomes thorium-233. The atomic number remains the same at 90, but the mass number increases by 1, resulting in { }_{90}^{233} ext{Th} .

First Beta Decay

In a beta decay, a neutron is converted into a proton, increasing the atomic number by 1 while the mass number remains constant. Therefore, thorium-233 undergoes beta decay and becomes protactinium-233 (^{233}_{91} ext{Pa}) .

Second Beta Decay

The protactinium-233 nucleus undergoes another beta decay. Again, a neutron is converted into a proton, increasing the atomic number by 1. Therefore, protactinium-233 becomes uranium-233 (^{233}_{92} ext{U}) .

Key concepts

Neutron Absorption

Neutron absorption is a fundamental process in nuclear chemistry, altering a nucleus by capturing a neutron. This process is crucial in nuclear reactions and can change the mass number of an element. When a nucleus absorbs a neutron, the atomic number stays the same, since no protons are added or removed. However, the mass number, which is the sum of protons and neutrons, increases by one.
For instance, when thorium-232, represented as \({ }_{90}^{232} \text{Th}\), absorbs a neutron, it turns into thorium-233, \({ }_{90}^{233} \text{Th}\). Here, the atomic number remains 90, while the mass number becomes 233 because one more neutron is added to the nucleus.

Beta Decay

Beta decay is a type of radioactive decay uncovered during nuclear reactions. In beta decay, a neutron in the nucleus converts into a proton and releases a beta particle, which is an electron, and an antineutrino. This transformation increases the atomic number by one, as one proton is added, but the mass number remains constant since the total count of nucleons (protons + neutrons) stays the same.
A real-world example of this is seen in thorium-233, \({ }_{90}^{233} \text{Th}\), undergoing beta decay. It changes into protactinium-233, \({ }_{91}^{233} \text{Pa}\), as a neutron turns into a proton. A second beta decay of protactinium-233 leads to the formation of uranium-233, \({ }_{92}^{233} \text{U}\), with another increase in the atomic number.

Atomic Number

The atomic number is a defining property of an element in the periodic table. It is equal to the number of protons in the nucleus of an atom. The atomic number determines the chemical element's identity and its position on the periodic table.
For example, the atomic number of thorium is 90, as denoted in \({ }_{90} \text{Th}\). Beta decay causes a change in the atomic number because when a neutron is converted into a proton, the count of protons—hence the atomic number—increases by one. Therefore, when thorium-233 undergoes beta decay, its atomic number goes from 90 to 91, forming protactinium. Another beta decay transforms protactinium into uranium, increasing the atomic number from 91 to 92.

Mass Number

Mass number is another critical characteristic of an atom, representing the total number of protons and neutrons in the nucleus. This number gives an indication of the atom's mass and is typically not affected by beta decay since only the atomic number changes.
When a neutron is absorbed by a thorium-232 nucleus, its mass number increases by one, going from 232 to 233. In contrast, during beta decay, the mass number remains unchanged, even though the atomic number rises. Thus, both protactinium-233 and uranium-233 have the same mass number of 233, demonstrating that the number of nucleons stays constant during beta decay.