Half-Life and Decay Rates: Understanding Radioactive Substances, Slides of Physics

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Half

Life

Decay

Rates

The number of particles decaying in a short period of time is proportional to the number of particles.

The decay constant is

The decay rate or activity is the rate of change.

Activity decreases as time increases

t

N

N

N t N A      

Half

Life

The relationship for decay gives rise to an exponential relation.

Decay constant is fixed for a decay reaction - Decay is usually expressed as a half

life

Time for half a sample to decay - Half ‐ life constant for the nucleus type t N N      t e N N    0 T e    1 2   693 . 0 2 ln   T

Exponential

Decay

Half

life

applies

to

each

sample

separately.

This

is

exponential

decay

Specific

Activity

Physical variables are often normalized to the mass.

Described as “specific” - Specific activity is the activity of a sample divided by the mass. - Units Bq g ‐^1 or  Ci g ‐^1

In solution expressed per unit volume: pCi L ‐^1

For a pure radionuclide:

Normal soil has a few pCi/g - Drinking water has a recommended limit of

pCi/L of 226 Ra

(^228) Ra. MT M N m SA 23 23 10 (^17). 4 10 (^02). 6       

Figure

14

C is a very rare isotope with a half-life of 5730 years.

In a living organism, the

14

C activity is 0.25 Bq.

When the organism dies, the

14

C exchange with the

environment stops. 

14

C starts decaying.

By measuring the

14

C /

12

C ratio we can estimate the

age of the sample.

Radiocarbon

Carbon

14

C)

is a radioactive isotope.

Beta decay - Half ‐ life 5730 years - Carbon

is produced in the atmosphere by cosmic rays.

Absorbed by organisms - Stops at death - Fraction of (^14)

C

to (^12)

C

establishes the date of an object.

p next

n

C

N

14 14

e

N

C

14 14