Question

May be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant for plutonium-240 is k =0.00011. What is the half life years

Answer 1

Answer:

The half life of the sample is 6301 years.

Step-by-step explanation:

The function used to model radioactive decay or exponential decay is,

$Q(t)=Q_0e^{-k\cdot t}$

Where,

Q(t) = Quantity after t time

Q₀ = Initial

k = decay constant

t = time period

As after an half life, the amount becomes half so,

$\Rightarrow \dfrac{Q_0}{2}=Q_0e^{-0.00011\cdot t}$

$\Rightarrow \dfrac{1}{2}=e^{-0.00011\cdot t}$

Taking natural log of both sides,

$\Rightarrow \ln \dfrac{1}{2}=\ln e^{-0.00011\cdot t}$

$\Rightarrow \ln \dfrac{1}{2}={-0.00011\cdot t}\times \ln e$

$\Rightarrow \ln \dfrac{1}{2}={-0.00011\cdot t}\times 1$

$\Rightarrow {-0.00011\cdot t}=\ln \dfrac{1}{2}$

$\Rightarrow t=\dfrac{\ln \dfrac{1}{2}}{-0.00011}$

$\Rightarrow t=6301.3\approx 6301\ years$