Determine the half-life of a nuclide that loses 38.0% of its mass in 387 hours.

Question

Quizplus · Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the sample to decay. In this case, the nuclide lost 38.0% of its mass, which means that it has 62.0% of its original mass remaining. We can set up an equation using the formula for exponential decay:

0.62 = (1/2)^(t/h)

where t is the time in hours and h is the half-life in hours. Solving for h, we get:

h = t / log2(1/2)

h = t / (-0.693)

h = -1.443t

Plugging in the given values:

0.62 = (1/2)^(387/h)

Taking the log of both sides:

log(0.62) = -387/h * log(2)

h = -387 / (log(0.62) / log(2))

h ≈ 561 hours

Therefore, the half-life of the nuclide is approximately 561 hours.

Determine the Half-Life of a Nuclide That Loses 38