Half-life of isotope from decay rate measurements

[MrChaos]

Hello :)

I came across a question and I haven't been able to solve it so far. It would be great if maybe someone could give me a few tips.

Here is the question:

Measurements of the radioactivity of a certain isotope tell you that the decay rate
decreases from 8305 decays per minute to 3070 decays per minute over a period of 5.00
days.

What is the half-life T1/2 of this isotope?

How can I get the right answer for this question? I never really worked with those half-life
questions. I am still interested how it works.

thanks :)

 

[kuruman]

Hi MrChaos and welcome to PF. Please observe our rules and use the template for posting requests for help with homework.

What equation do you know that relates activity to time and half-life>

 

[MrsChaos]

umm...

N = N₀ e^-lambda*t

i'm not sure if this ones right

T_1/2= ln 2/lambda

 

[MrsChaos]

mission impossible now complete
on my last attempt i got it right

ln (R_1/R_2)= lambda*deltat
ln (8305/3070)= lambda*5days
0.995180181= lambda*5days
0.995180181*1/5 = 0.19903636 = lambda

lambda*T= ln 2= 0.6931
0.6931/0.19903636= T
T_1/2= 3.482283978
= 3.48 days

:)