## Sciencium-380 has a half-life of 3 days. If you started with a 100 gram sample, how much Sciencium-380 will remain after 9 days?

Question

Sciencium-380 has a half-life of 3 days. If you started with a 100 gram sample, how much Sciencium-380 will remain after 9 days?

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2 months 2021-07-25T05:33:27+00:00 2 Answers 4 views 0

12.5 grams

Explanation:

Solution:-

– By definition, the half-life is the amount of time t that a substance of mass M   to decay to half its its initial mass.

– We are given the mass of the Sciencium-380, M = 100 g

– The half-life for the radioactive isotope is, h = 3 days

– The amount of mass left after t = 9 days.

– We will first estimate the number of half-lives that have passed in te duration of t = 9 years.

– The number of half lives are:

n = t / h

n = 9 / 3

n = 3

For every half life the mass is halved or mathematically the mass ( m ) of a substance remaining after ” n ” number of half lives can be expressed as:

m = M*0.5^n

– Plug in the given values and evaluate the mass ( m ) of the substance after n = 3 half lives.

m = 100*0.5^3

m = 12.5 grams.

Answer: We are left with 12.5 grams of Sciencium after 3 half lives have passed.

2. Answer: 12.5 grams will remain.

Explanation:

The half life time means that if we start with a quantity A of a given subtance/material, after the half time we will have half that quantity, or A/2.

We know that the half life of Sciencium-380 is 3 days.

So if we have 100 grams, after 3 days we will have 100/2 = 50 grams.

After other 3 days we will have 50/2 = 25 grams

After other 3 days we will have 25/2 = 12.5 grams.

So if we start with 100 grams, after 9 days we will have 12.5 grams.