Half-Life Problem

[msmarvelous]

Hi,
I'm pretty comfortable using logarithms, I just need clarification on how to solve half-life problems. Just show me the steps that you took to solve the problem.

The half-life of a certain substance is 30 hours. About how many hours will it take for an initial amount of 8 grams to decay to 2.5 grams?

Thanks!

 

[stapel]

You have the general equation, A = Pe[sup:u4bs46tl]rt[/sup:u4bs46tl] and the data point (30, P/2). Plug these values in for "t" and "A", and solve for the decay constant "r".

Then plug this value in for "r", "8" in for "P", and "2.5" in for "A", and solve for "t". :wink:

 

[mmm4444bot]

… Just show me the steps that you [take] to solve …

Hello Ms. Marvelous:

Step 1: Write a generic equation that models half-life decay

Step 2: Substitute the given values into this equation

Step 3: Solve for the unknown

Here's one of the generic models.

A = M * (1/2)^(t/H)

M = the initial amount at time t = 0

A = the amount remaining after t units of time

H = the half-life (in same units of time as t)

t = the time variable

Here's an example.

How many months are required for 500 kilograms of Stuffinium to become 100 kilograms of Stuffinium, if its half-life is 2 months?

M = 500

A = 100

H = 2

t = elapsed time (in months)

100 = 500 * (1/2)^(t/2)

(1/2)^(t/2) = 1/5

t = 2 * log_[1/2](1/5)

t = 2 * ln(5)/ln(2)

t ? 4.6439

It takes about 4.6 months for Stuffinium to decay from 500 to 100 kilograms.

Cheers,

~ Mark