Radioactive Decay

Step 1: Use the radioactive decay law.
The number of disintegrations

N

at any time

t

is given by:

N%20%3D%20N_0%20e%5E%7B-%5Clambda%20t%7D

where

N_0

is the initial disintegration rate,

%5Clambda

is the decay constant, and

t

is the time.
Step 2: Set up the equation.
At

t%20%3D%2020

hours,

N%20%3D%2010%5E%7B10%7D

, and at

t%20%3D%2030

hours,

N%20%3D%205%20%5Ctimes%2010%5E9

. Using the decay law:

%5Cfrac%7BN(t%3D30)%7D%7BN(t%3D20)%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%2010%5E9%7D%7B10%5E%7B10%7D%7D%20%3D%20e%5E%7B-%5Clambda%20(30-20)%7D

0.5%20%3D%20e%5E%7B-10%20%5Clambda%7D

Taking the natural logarithm of both sides:

%5Cln(0.5)%20%3D%20-10%20%5Clambda

%5Clambda%20%3D%20-%5Cfrac%7B%5Cln(0.5)%7D%7B10%7D%20%3D%200.0693%20%5C%2C%20%5Ctext%7Bhr%7D%5E%7B-1%7D

Chapter Questions
1 MCQs