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Element x decays radioactively with a half life of 13 minutes. If there are 400 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 4 grams?.

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Ayuneidn

The time needed for a 400-grams radioactive element with half-life of 13 minutes to decay to 4 grams is 86.4 minutes.

The half-life formula of a decay system is given by:

A = Ao x (0.5)^(t/h)

Where:

A = final amount

Ao = Initial amount

t = time period

h = half-life

Parameters given in the problem:

h = 13 minutes

Ao = 400 grams

A = 4 grams

Plug these parameters into the formula:

4 = 400 x (0.5)^(t/13)

(0.5)^(t/13) = 0.01

t/13 x log(0.5) = log (0.01)

t/13 = 6.64

t = 6.64 x 13 = 86.4 minutes

Hence, it takes 86.4 minutes for the element X to decay to 4 grams.

Learn more about half life here:

https://brainly.com/question/25750315

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