High School

Determine the half-life of a nuclide that loses 82.0% of its mass in 46.5 days.

a) 24 days
b) 162 days
c) 18.8 days
d) 25.3 days
e) 7.8 days

Answer :

Final answer:

The half-life of the nuclide is 24.0 days.

Explanation:

The half-life of a nuclide is the time it takes for half of the sample to undergo radioactive decay. To determine the half-life, we can use the formula:

Half-life = (0.693 / decay constant)

Here, since the nuclide loses 82.0% of its mass, the remaining mass is 100% - 82.0% = 18.0%. The remaining mass after every half-life is given by the equation:

Remaining mass = Initial mass * (1 - 0.82)

We can calculate the decay constant using the equation:

decay constant = 0.693 / half-life

Therefore, the half-life is:

Half-life = 0.693 / (log(100% / 18.0%) / log(2)) = 24.0 days

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