How do you do this half-life problem..?

Question

I've tried to the problem but i don't how (my teacher never explained and the book isn't very helpful)

A 100-mg technetium-99m sample is used in a medical study. How much of the technetium-99m sample remains after 24 hr? the half-life of technetium-99m is 6.0 hr

Thanks in advance!

Answer 1

There is an equation that you can use for 1/2 life problems
n = N * (1/2)^(t/p)
I'm not sure if those are the universally accepted variables, but that is the equation providing.
N = intial quantity of material (could be moles, grams, etc)
n = final quantity of material (will be same units as N)
t = time passed since initial measurement (N) was made.
p = 1/2 life time of material.

Now that we have that equation...
N = 100mg
n = unknown
t = 24h
p = 6h

Plug it in
n = 100mg* (1/2)^(24/6)
n = 100mg * (1/2)^(4)
n = 100mg * (1/16)
n = 6.25mg
After 24 hours only 6.25mg of Technetium will remain.

Answer 2

Use this half-life formula: A(1/2)^(t/k) where k is the time needed for one half life, and t is the time passed so for ur problem, it'll be 100(1/2)^(24/6)
Which is equal to 100(1/2)^4 = 6.25 mg

Answer 3

start with 100mg

100mg -6hr-> 50mg -6hr-> 25mg -6hr-> 12.5mg -6hr-> 6.25mg