Chapter 40, Problem 26A

(a)

To determine

The Rank: The product nuclei of the given reactions by atomic number from greatest to least.

Explanation of Solution

Introduction:

The atomic number of the radioactive material decrease by two units due to the ejection of the alpha particle and the atomic number of the radioactive material increases by one unit due to the ejection of the beta particle.

The atomic number of ${}_{92}^{238}\text{U}$ decreases by two units by alpha decay. So, the atomic number of the new atom becomes 90.

The atomic number of ${}_{94}^{239}\text{Pu}$ decreases by two units by alpha decay. So, the atomic number of the new atom becomes 92.

The atomic number of ${}_{90}^{239}\text{Th}$ Increases by one unit by beta decay. So, the atomic number of the new atom becomes 91.

The atomic number of ${}_{93}^{239}\text{Np}$ Increases by one unit by beta decay. So, the atomic number of the new atom becomes 94.

Conclusion:

Thus, the ranking of the isotopes by the number of the atomic number of the final product is D, B, C, A.

(b)

To determine

The Rank: The product nuclei of the given reactions by the number of neutrons from greatest to least.

Explanation of Solution

Introduction:

The number of neutrons in the nucleus of an atom is equal to the difference of a mass number and the atomic number of the atom.

The atomic number of the ${}_{92}^{238}\text{U}$ decreases by two units and the atomic mass number by four units due to alpha decay, so the atomic number of the new atom becomes 90 and the mass number is 234. The number of neutrons in the product nuclei is 144.

The atomic number of the ${}_{94}^{239}\text{Pu}$ decreases by two units and the atomic mass number decreases by four units due to alpha decay.So the atomic number of the new atom becomes 92 and the atomic mass number is 235. The number of neutrons in the product nuclei is 143.

The atomic number of the ${}_{90}^{239}\text{Th}$ increases by one unit by beta decay, so the atomic number of the new atom becomes 91. The number of neutrons in product nuclei is 148.

The atomic number of the ${}_{93}^{239}\text{Np}$ increases by one unit by beta decay, so the atomic number of the new atom becomes 94.The number of neutrons in product nuclei is 145.

Conclusion:

The rank of the product nuclei of the given reactions by number of neutrons from greatest to least is:

C, D A, B.