A certain radioactive material that initially has a

Kaylee May Fontejon

Kaylee May Fontejon

Answered question

2022-05-26

A certain radioactive material that initially has a mass of 2,340 grams has a half life of 6 years.What will be its mass after 20 years,assuming that its decay rate is exponential

Answer & Explanation

Eliza Beth13

Eliza Beth13

Skilled2023-05-17Added 130 answers

To solve the given problem, we can use the formula for exponential decay, which is given by:
N(t)=N0·eλt
Where:
N(t) represents the remaining mass at time t
N0 represents the initial mass
λ represents the decay constant
t represents the time elapsed
Given:
N0=2,340 grams (initial mass)
Half-life (T12) = 6 years
The decay constant can be calculated using the formula:
λ=ln(2)T12
Substituting the given values into the formula, we have:
λ=ln(2)6
Now, we can substitute the values of N0, λ, and t into the exponential decay equation to find the remaining mass after 20 years:
N(t)=N0·eλt
N(20)=2,340·e(ln(2)6)·20
To find the value, we can plug it into a calculator or compute it using the given values:
N(20)2,340·e(ln(2)6)·201,383.88 grams (rounded to two decimal places)
Therefore, the mass of the radioactive material after 20 years, assuming exponential decay, will be approximately 1,383.88 grams.

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