Answer:
t = 4.41 10⁻⁴ years
Explanation:
For this exercise we must use the concept of average life time, which is the time in which the quantity and substance decays in half
[tex]T_{1/2}[/tex] = ln2 / λ
Let's calculate the decay constant of plutonium
λ = ln2 / [tex]T_{1/2}[/tex]
λ = ln 2 / 2.44 10⁵
λ = 2.84 10⁻⁶ s⁻¹
Radioactive decay is a first order process
N = No e (-λ t)
Where N is the number of nuclei, the mass is this by molecular weight
m = N PM
m / PM = m₀ / PM e (- λ t)
m / m₀ = e (- λ t)
-λ t = ln (m / m₀)
t = -1 /λ ln (m/m₀)
t = - 1 / 2.84 10⁻⁶ ln (0.1 / 0.35)
t = 4.41 10⁻⁴ years
The time taken for the radioactive plutonium−239 having a half-life of 2.44×10⁵ years to decay from 3.50×10² g to 1×10² g is 4.41×10⁵ years
2ⁿ = N₀ / N
2ⁿ = 3.50×10² / 1×10²
2ⁿ = 3.5
Take the log of both side
Log 2ⁿ = Log 3.5
nLog 2 = Log 3.5
Divide both side by Log 2
n = Log 3.5 ÷ Log 2
n = 1.807
t = n × t½
t = 1.807 × 2.44×10⁵
t = 4.41×10⁵ years
Learn more about half life:
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