Question

50V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of 1.00 kg of 50V is 1.75 Bq. What is the half-life in years?

a) 2.70 x 10¹⁷ years
b) 2.85 x 10¹⁷ years
c) 3.00 x 10¹⁷ years
d) 3.15 x 10¹⁷ years

Answer 1

The half-life of 50V can be calculated using its decay activity and the number of 50V atoms in 1.00 kg, which requires additional constants and calculations.

Step-by-step explanation:

The half-life of a radioactive isotope can be determined by using its decay activity and the number of atoms. In this question, we need to calculate the half-life using the given activity of 1.75 Bq for 1.00 kg of 50V. The decay activity (A) is related to the decay constant (λ) and number of atoms (N) by the formula A = λN. Furthermore, the decay constant is related to the half-life (T1/2) by the formula λ = ln(2)/T1/2.

By rearranging these formulas and substituting the known values, we can calculate the half-life. However, the precise calculation would require additional details like the number of atoms in 1 kg of 50V, which depends on Avogadro's number and the atomic mass of 50V. Without the explicit values, one cannot definitively calculate the half-life from the activity alone, but typically we could solve for T1/2 using the mentioned relationships if we were given or could derive all necessary values.