The radiochemist, Will I. Glow, studied thorium-232 and found that 2.82 × 10^-7 moles emitted 8.42 × 10⁶ α particles in one year. What is the decay constant for thorium-232?

Question

Quizplus · Accepted Answer

The decay constant, denoted by λ, is the fraction of atoms that decay per unit time. It is related to the number of decays per unit time, denoted by N, through the equation N = λN0, where N0 is the initial number of atoms.

In this problem, we are given the number of decays per unit time (8.42 × 10^16 α particles per year) and the number of atoms (2.82 × 10^17 moles of thorium-232). We need to find the decay constant.

First, we need to convert the number of moles to the number of atoms. One mole of an element contains Avogadro's number of atoms, which is approximately 6.022 × 10^23. Therefore, 2.82 × 10^17 moles of thorium-232 contain:

2.82 × 10^17 moles × 6.022 × 10^23 atoms/mole = 1.698 × 10^41 atoms

Using the equation N = λN0, we can solve for λ:

N = λN0
8.42 × 10^16 α particles/year = λ (1.698 × 10^41 atoms)
λ = 8.42 × 10^16 α particles/year / 1.698 × 10^41 atoms
λ = 4.96 × 10^-11 year^-1

Therefore, the best choice is B: 4.96 × 10^-11 year^-1.

The Radiochemist, Will I