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

The half-life of plutonium-240 is approximately 6300 years, calculated using the equation t₁/₂ = 0.693 / k, where k is the decay constant.

Step-by-step explanation:

The concept of half-life is crucial in understanding radioactive decay, such as for isotopes like plutonium-240. To calculate the half-life (t₁/₂) using the decay constant (k), you can use the equation ℓ = 0.693 / k. Given that the decay constant k for plutonium-240 is 0.00011, the half-life can be calculated as follows:

t₁/₂ = 0.693 / 0.00011
t₁/₂ ≈ 6300 years

Therefore, the half-life of plutonium-240 is approximately 6300 years. This means that after 6300 years, half of the original quantity of plutonium-240 would remain, and after another 6300 years, only a quarter would be left, continuing the pattern of exponential decay.

Answer 2

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 (Q_0)/(2)=Q_0e^(-0.00011\cdot t)`

`\Rightarrow (1)/(2)=e^(-0.00011\cdot t)`

Taking natural log of both sides,

`\Rightarrow \ln (1)/(2)=\ln e^(-0.00011\cdot t)`

`\Rightarrow \ln (1)/(2)={-0.00011\cdot t}* \ln e`

`\Rightarrow \ln (1)/(2)={-0.00011\cdot t}* 1`

`\Rightarrow {-0.00011\cdot t}=\ln (1)/(2)`

`\Rightarrow t=(\ln (1)/(2))/(-0.00011)`

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