Question

97.
Calculate the Uranium X1 decay
constant from its halflife. How long
would it take to decompose 30
percent of the original sample?

Answer 1

Answer:

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Explanation:

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

N/N₀ = e^{-\lambda t}e

−λt

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

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

−λt

0.3 = e^{-\lambda t}e

−λt

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.

@ngel....