Question

Element X decays radioactively with a half life of 15 minutes. If there are 960 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 295 grams?

Answer 1

An equation is formed of two equal expressions. It will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The radioactive decay of an element is given by the formula,

$N = N_0 \cdot e^{-\lambda t}$

Given the half-life of the element is 15 minutes, therefore, we can write,

$\dfrac12 = e^{-\lambda\times 15}\\\\\ln (0.5) = -\lambda\times 15\\\\\lambda = 0.0462$

Now, the time it will take for 960 grams to decay to 295 grams is,

$295 = 960 \cdot e^{-0.0462 \times t}\\\\\ln (\dfrac{295}{960}) = -0.0462 \times t\\\\t = 25.54\rm\ minutes$

Hence, it will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

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