Determining half life from a half life graph

today I'm going to show you a really

quick and easy way to determine the

half-life if given a graph you can

always feel free to reference this first

page which actually has all of the

directions but I'm just going to go

through an example with these steps so

here's an example um your half-life

graph that you'd be determining the

half-life from would have some type of

an amount maybe it's counts maybe it's

number of atoms but some type of count

unit on the y axis versus time on your x

axis and you should have this kind of

logarithmic graph that would be produced

so how would I use this to figure out

the half-life so all you do is just

select any point on your graph to start

with I find the starting point sometimes

most convenient in this case it would be

at 80 and then all I'm gonna do is I'm

going to go down to half of 80 because

after one half-life half of my starting

amount should be present so half of 80s

for T so I'm just gonna draw a vertical

line down to 40 and then I'm gonna go

across until I hit my best fit curve

again and the length of this horizontal

line should give me the half-life so

it's about 0 to 6 so it's about 6 days

that's my half-life you can pick any

graph any point on the graph to start

with so let's say I started with 40 go

down to half of it which would be 20 and

go back until I touch the graph again

and again the length of this horizontal

line is my half-life in this case I'm

going from 6 to 12 days so again that's

a half-life of 6 days if you have a

correct graph for a first-order decay

which is what radioactivity is you

should be getting a relatively constant

half-life given some experimental error

so just showing again with another

example here's another example okay here

I'm starting I can pick any point on the

graph to start with point pick a point

on your best-fit curve go down to half

and go across and the length again of

that horizontal line gives me the

half-life in this case two dates and I

can do that again at any point on my

graph just to confirm for you down to 20

which is half of it and across still

gives me two days okay again just make

sure you're picking a point on your

actual best-fit line go down to 1/2

which would be what's left after a

half-life and then go across and the

length of that horizontal line it's your

half-life if you have to show your work

on the graph this is what it should kind

of look like