Answer:
67.6 years is the time the isotope take to decay from 0.900g to 0.170g
Explanation:
The radioactive decay follows first order law:
Ln [A] = -kt + ln[A]₀
Where [A] is concentration after time t,
k is decay constant:
k = ln 2 / t(1/2)
k = ln2 / 28.1 years
k = 0.02467 years⁻¹
[A]₀ = Initial concentration.
We can replace concentration and use the mass of the isotope:
Ln [A] = -kt + ln[A]₀
Ln [0.170g] = -0.02467 years⁻¹t + ln[0.900g]
-1.667 = -0.02467 years⁻¹t
t =
The time required for the sample to reduce to 0.170 grams has been 67.75 years.
Half-life can be defined as the times required by the substance to reduce to half of its initial concentration.
The half-life can be expressed as:
Amount left = Initial amount [tex]\times[/tex] [tex]\rm \dfrac{1}{2}^\dfrac{time}{Half-life}[/tex]
From the given:
0.17 g = 0.9 [tex]\rm \times\;\dfrac{1}{2}^\dfrac{t}{28.1}[/tex]
[tex]\rm \dfrac{0.17}{0.9}[/tex] = [tex]\rm \dfrac{1}{2}^\dfrac{t}{28.1}[/tex]
0.188 = [tex]\rm (0.5)^\dfrac{t}{28.1}[/tex]
Taking log on both the sides,
log 0.188 = [tex]\rm \dfrac{t}{28.1}\;\times[/tex] log 0.5
2.411 = [tex]\rm\dfrac{t}{28.1}[/tex]
t = 2.411 [tex]\times[/tex] 28.1 years
Time = 67.75 years.
The time required for the sample to reduce to 0.170 grams has been 67.75 years.
For more information about half-life, refer to the link:
https://brainly.com/question/24710827
