Question

Q 79 Calculate the Uranium X, decay constant from its half - life. How long would it take to decompose 30 percent of the original sample?
14.01 days
Ops: A.
B.
12.8 days
C.
D.
12.61 days
13.9 days​

Answer 1

The time taken to decompose is:

t = 1.203/0.693 × t1/2

Explanation:

The number of Uranium X is given by the formula:

N = N₀ $e^{-\lambda t}$

N/N₀ = $e^{-\lambda t}$

From question, we need to decompose 30 percent of the original sample.

30/100 = $e^{-\lambda t}$

0.3 = $e^{-\lambda t}$

ln (0.3) = -λt

-1.203 = -λt

1.203 = λt

t = 1.203/λ → (equation 1)

Now, the decay constant and half time is given by the formula:

λ = 0.693/t1/2 → (equation 2)

On substituting the equation (2) in (1), we get,

t = 1.203/(0.693/t1/2)

∴ t = 1.203/0.693 × t1/2

From question, the half life is not given.

The value of the half life is substituted in the above equation to calculate time taken to decompose.