At the beginning of an experiment, a scientist has 356 grams of radioactive goo..?

Question

At the beginning of an experiment, a scientist has 356 grams of radioactive goo. After 225 minutes, her sample has decayed to 5.5625 grams.

What is the half-life of the goo in minutes? 

Find a formula for G(t) the amount of goo remaining at time t?

How many grams of goo will remain after 17 minutes?

Answer 1

The radioactive decay is given by

N = N₀ e ^- λt

Where  λ = Decay constant

Decay constant is related to half life as

 λ= 0.693/ T, where T = Half life

Plug in values

5.5625 = 356 e ^- λ*225

356/5.5625 = e ^λ*225

64 = e ^λ*225

ln 64 = λ*225

4.1588830 = λ*225

Gives λ = 4.1588830 /225 = 0.018483

So Half life = T = 0.693 / 0.018483

T = 37.59 Min ( Half Life )

For after 17 Min

N = 356 ( e ^{- 0.018483* 17})

Find N from here

N= 356 ( e ^-0.3142)

find N from here

N = 356 * 0.73037

N = 260 gm