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:


ln[N]t = -kt + ln[N]0


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:


t12 = ln 2k


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)
View Complete Written Solution
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.)

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.