The half-life of silver-108m is approximately 130 years. 1. How much of a 4 gram sample of silver-108m would remain after 27 years? Round to three decimal places.
2. How much of a 4 gram sample of silver-108m would remain after 79 years?

(1) 3.467 grams of a 4-gram sample of silver-108m would remain after 27 years.

(2) 2.632 grams of a 4-gram sample of silver-108m would remain after 79 years.

Step-by-step explanation:

We are given that the half-life of silver-108m is approximately 130 years.

We can assume this situation as an exponential decay where A(t) be the amount of sample of silver-108m that remain after t years.

Let be the initial amount and r will be the decay constant (which will be a negative number)

Now, it is stated that the half-life of silver-108m is approximately 130 years, this means any amount after this time period will reduce to (/2), that is;

Taking log on both sides, we get;

r = -0.0053

(1) We have to find how much of a 4-gram sample of silver-108m would remain after 27 years, that is;

Here, t = 27 years, = 4 grams and r we have calculated above.

So,

A(27) = 3.467 grams

Hence, 3.467 grams of a 4-gram sample of silver-108m would remain after 27 years.

(2) We have to find how much of a 4-gram sample of silver-108m would remain after 79 years, that is;

Here, t = 79 years, = 4 grams and r we have calculated above.

So,

A(79) = 2.632 grams

Hence, 2.632 grams of a 4-gram sample of silver-108m would remain after 79 years.

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step-by-step explanation:

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