# Problem: Nuclear decay is a first-order kinetic process. Therefore, If N0 nuclei are present at time t = 0, the number remaining at time t is given by the equation:N = N0e-ktThe decay of radioactive nuclei with known half-lives enables geochemists to measure the age of rocks from their compositions. For example, it is known that 238U decays to 206Pb with a half-life of 4.51 x 109 years.Suppose that a uranium-bearing rock was deposited 1.8 billion (1.80 x 109) years ago and remained geologically unaltered to the present time.What fraction of the starting 238U would remain after 1.8 billion years? Please circle your answer.

###### FREE Expert Solution

We’re being asked to calculate the fraction of the starting 238U would remain after 1.8 billion years

Recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half

The half-life of a first-order reaction is given by:

where:

t1/2 = half-life

k = decay constant

We don’t know the decay constant but we can calculate it from the given values.

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the rate law for first-order reactions is:

where:

Nt = amount at time t

k = decay constant

t = time

N0 = initial amount

We use the following steps to solve the problem:

Step 1. Calculate the decay constant

Step 2. Calculate the fraction remaining

85% (348 ratings) ###### Problem Details

Nuclear decay is a first-order kinetic process. Therefore, If N0 nuclei are present at time t = 0, the number remaining at time t is given by the equation:

N = N0e-kt

The decay of radioactive nuclei with known half-lives enables geochemists to measure the age of rocks from their compositions. For example, it is known that 238U decays to 206Pb with a half-life of 4.51 x 109 years.

Suppose that a uranium-bearing rock was deposited 1.8 billion (1.80 x 109) years ago and remained geologically unaltered to the present time.