Question

There is more than one isotope of natural uranium. If a researcher isolates 1.00 mg of the relatively scarce 235U and finds this mass to have an activity of 80.0 Bq, what is its half-life in years?

a) 6.80 x 10⁸ years
b) 6.95 x 10⁸ years
c) 7.10 x 10⁸ years
d) 7.25 x 10⁸ years

Answer 1

To find the half-life of 235U, use the decay equation and the given data of activity and mass of the isotope. Calculate the number of radioactive atoms and the decay constant, then substitute them into the half-life equation.

Step-by-step explanation:

To find the half-life of 235U, we can use the decay equation, which relates the activity of a radioactive sample to the decay constant and the number of radioactive atoms:

Activity = Decay Constant x Number of Radioactive Atoms

Since we know the activity (80.0 Bq) and the mass of 235U (1.00 mg), we can calculate the number of radioactive atoms and substitute it into the decay equation:

Number of Radioactive Atoms = (1.00 mg / 235 atomic mass unit) x (6.02 x 10^23 atoms/mole) x (1 mole/10^3 mg)

The decay constant can be determined from the half-life equation:

Half-life = ln(2) / Decay Constant

From the given data, we can calculate the half-life of 235U:

Half-life = ln(2) / Decay Constant