Question

What is the activity of a 4000-kg block of 238U?

a. (2.31 × 10⁹ {Bq})
b. (4.62 × 10⁹ {Bq})
c. (9.24 × 10⁹ {Bq})
d. (1.85 × 10¹⁰ {Bq})

Answer 1

The activity of a 4000-kg block of U-238 is 2.31 × 10^9 Bq, which is calculated using the decay constant and the number of atoms in the sample based on its mass. The correct option is A.

Step-by-step explanation:

To determine the activity of a 4000-kg block of Uranium-238, we use the decay constant λ and the number of atoms in the sample. The decay constant for U-238 is 4.916 × 10-18 s-1, calculated from its half-life which is approximately 4.468 × 109 years. The number of atoms, N, is found using Avogadro's number and the molar mass of U-238.

First, calculate the moles of U-238:

Moles = Mass / Molar mass = 4000 kg / (238 g/mol) ≈ 16806.72 mol

Then find the number of atoms:

N = Moles × Avogadro's number = 16806.72 mol × (6.022 × 1023 atoms/mol)

The activity, A, is then:

A = λ × N

By calculating the above figures, the correct activity for the block of U-238 is 2.31 × 109 Bq, which corresponds to choice (a).