Determine the half-life of a nuclide that loses 38.0% of its mass in 427 hours.

Question

Quizplus · Accepted Answer

The half-life of a radioactive substance is defined as the time it takes for half of the initial mass to decay. To determine the half-life, we can use the following equation:

N = N0 (1/2)^(t/t1/2)

where N is the final amount, N0 is the initial amount, t is the time elapsed, and t1/2 is the half-life.

We are given that the nuclide loses 38.0% of its mass, so the remaining mass is 62.0% of the initial mass. Therefore, we can set up the following equation:

0.62N0 = N0 (1/2)^(t/t1/2)

Simplifying this equation, we get:

(1/2)^(t/t1/2) = 0.62

Taking the logarithm of both sides, we get:

t/t1/2 = log(0.62) / log(1/2)

t1/2 = t / (log(0.62) / log(1/2))

Plugging in the given values, we get:

t1/2 = 427 hours / (log(0.62) / log(1/2)) = 619 hours

Therefore, the half-life of the nuclide is 619 hours. Thus the correct answer is C.

Determine the Half-Life of a Nuclide That Loses 38