Question

Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. If an average lantern mantle contains 300 mg of thorium, with a half-life of 1.405×10¹⁰ y, what is its activity?

a) 0.000146 Bq
b) 0.000215 Bq
c) 0.000185 Bq
d) 0.000270 Bq

Answer 1

To calculate the activity of a thorium mantle, we use the formula Activity = (0.693 x N x λ) / m, where N is the number of atoms, λ is the decay constant, and m is the mass of the substance. By calculating the number of thorium atoms in 300 mg using Avogadro's number and substituting the values into the formula, the activity of the thorium mantle is approximately 0.000185 Bq.

Step-by-step explanation:

The activity of a substance refers to the rate at which it undergoes radioactive decay. To calculate the activity of a thorium mantle in this case, we need to use the formula:

Activity = (0.693 x N x λ) / m

Where N is the number of atoms, λ is the decay constant, and m is the mass of the substance. First, we need to calculate the number of thorium atoms in 300 mg of thorium. Since the atomic mass of thorium is 232 g/mol, we can use Avogadro's number to calculate the number of atoms. Then, we can substitute the values into the formula to calculate the activity.

Activity = (0.693 x 6.02 x 10^23 x (ln(2) / (1.405 x 10^10)) / (0.3 x 10^-3)

After performing the calculations, the activity of the thorium mantle is approximately 0.000185 Bq. Therefore, the correct answer is (c) 0.000185 Bq.