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A certain radioactive element has a half-life of one hour. If you start with 40.0 grams of the element at noon, how much of the radioactive element will be left at 2 p.m.?


A.) 20.0 grams

B.) 10.0 grams

C.) 5.0 grams

D.) 0.0 grams

Verified Answer :

If you start with 40.0 grams of the element at noon, 10.0 grams
radioactive element will be left at 2 p.m. The correct answer between
all the choices given is the second choice or letter B. I am hoping that this
answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.

Answer:

B) 10.0 g

Explanation:

Given data:

Half life of the radioactive element = t1/2 = 1 hr

Initial amount, N0 = 40.0 g

Time for radioactive decay. t = 2 hr (12 noon  to 2 P.M)

Formula:

The radioactive decay is expressed mathematically as:

\(N(t) = N(0)e^{\frac{-0.693t}{t1/2} }\)

where N(t) is the amount of the element left after time t

Substituting the appropriate vales in the above equation we get:

\(N(t) = 40.0 * e^{\frac{-0.693*2}{1} } = 10.0 g\)

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