Answer:
THE FRACTION OF THE SAMPLE REMAINING AFTER THREE HALF LIVES IS 0.125 OR 125/1000
Step-by-step explanation:
A radioactive isotope of mercury decay to gold with a disintegration constant of 0.0108 h^-1
To calculate the fraction of sample remaining after three half life, we first calculate the half life of the decay.
Half life = ln 2 / Y
Y = disintegration constant
So therefore,
half life = ln 2 / 0.0108
half life = 0.693 / 0.0108
half life = 64.18 hours.
So a decay occurs after 64.18 hours.
To calculate the fraction remaining after 3 half life:
N(t) = N(o) e ^-Yt
where t = 3 half life
So, N / No = e^-Y ( 3 t1/2)
Since t 1/2 = ln 2 / Y, so we can re-write the formula as:
Nt / No = e^-Y ( 3 ln 2/ Y)
Nt / No = e^-3 ln2
Nt / No = e^-3 * 0.693
Nt / No = e^-2.079
Nt / No = 0.125
So the fraction of the sample remaining after 3 half lives is 125/ 1000 or 0.125