Question

You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their half-lives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it. Neglect the activity of any daughter nuclides.

a) 3.70 x 10⁻⁵ Bq
b) 3.70 x 10⁻⁴ Bq
c) 3.70 x 10⁻³ Bq
d) 3.70 x 10⁻² Bq

Answer 1

The activity of the vase is approximately 4.09 x 10^8 Bq, which is closest to option d) 3.70 x 10^² Bq.

Identify the relevant isotope: Natural uranium consists mainly of three isotopes: U-238 (99.2742%), U-235 (0.7204%), and U-234 (0.0054%). We need to choose the one with the most significant contribution to the activity.

Calculate the number of atoms: Using the mass of uranium and the atomic mass of the chosen isotope, we can calculate the number of atoms present in the vase.

Determine the decay constant: Look up the decay constant (λ) for the chosen isotope.

Calculate the activity: Activity (A) is the number of decays per second occurring in the material. It can be calculated using the equation: A = Nλ, where N is the number of atoms and λ is the decay constant.

Relevant isotope: We choose U-238 since it has the highest abundance.

Number of atoms:

• Mass of uranium: 2.00 g
• Atomic mass of U-238: 238.0289 u
• Number of atoms (N): (2.00 g) / (238.0289 u/atom) ≈ 8.37 x 10^19 atoms

Decay constant: The decay constant (λ) of U-238 is 4.891 x 10^-11 s^-1.

Activity:

• Activity (A): Nλ ≈ (8.37 x 10^19 atoms) * (4.891 x 10^-11 s^-1) ≈ 4.09 x 10^8 Bq