Q 83 Calculate the Uranium X, decay constant from its half - life. How long would it take to decompose 30 percent of the original sample?Ops: A. 13.9 daysB. O 14.01 daysC 12.61 daysD. 12.8 days
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t = 1.203/0.693 × t1/2
Explanation:
The number of Uranium X is:
N = N₀ e^(λt)
So N/N₀ = e^(λt)
We need to decompose 30% of the original sample.
30/100 = e^(λt)
0.3 = e^(λt)
ln(0.3) = -λt
-1.203 = -λt
1.203 = λt
Therefore t = 1.203/λ ------------------(1)
The decay constant and half time is given by the formula:
λ = 0.693/t1/2 --------------(2)
Substituting 2 in 1, we get:
t = 1.203/(0.693/t1/2)
t = 1.203/0.693 * t1/2
The value of the half life (t1/2) should be substituted in the above equation to calculate the time taken to decompose.
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