# Problem: A sample of Tl-201 has an initial decay rate of 5.88×104 /s .How long will it take for the decay rate to fall to 303 /s ? (Tl-201 has a half-life of 3.042 days.)

###### FREE Expert Solution

We’re being asked to determine the time it takes for the decay rate of Tl-201 to fall from 5.88×104 /s to 303/s.

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

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration.

Also, 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:

We will do the following steps to solve the problem:

Step 1: Calculate the decay constant, k

Step 2: Calculate the time

82% (470 ratings) ###### Problem Details

A sample of Tl-201 has an initial decay rate of 5.88×104 /s .

How long will it take for the decay rate to fall to 303 /s ? (Tl-201 has a half-life of 3.042 days.)