Question

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​

Answer 1

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.