Chapter 40, Problem 49A

To determine

The nucleus results from the two successive beta decay of thorium.

Explanation of Solution

Introduction:

The number of protons in a nucleus of the new radioactive material increases due to beta decay from the nucleus of initial radioactive material. The number of protons in the nucleus describes the atomic number of the element, so the atomic number of the element also increases by one in beta decay.

The atomic number of ${}_{90}^{232}\text{Th}$ is 90. The atomic number of the radioactive material increase by two units in the two successive beta decay of the thorium. So, the atomic number of the new radioactive material becomes 92 and number of protons in the nucleus of new radioactive material is also 92.

The mass number in beta decay remains the same, but the mass number of new radioactive material increases by one unit also due to absorbing of one neutron by ${}_{90}^{232}\text{Th}$ . The mass number of the new nucleus becomes 233.

Conclusion:

Thus, the new nucleus results in the two successive beta decay of ${}_{90}^{232}\text{Th}$ is ${}_{92}^{233}\text{U}$ .