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5 grams of chucknorrisidium created, decays at a half-life of 16,000,000 Need 1 gram for experiments. How long before the is 1 gram remaining

Sagot :

Onyebuchinnajiidn

Answer:

the time taken for the element to remain 1 gram is 38,400,000 unit.

Step-by-step explanation:

Given;

initial mass, m = 5 g

half life, t = 16,000,000 unit

The time taken for the element to remain 1 gram is calculated as;

          mass remaining                                      time

             5 g                                                        0

             2.5 g                                                    16,000,000

             1.25 g                                                   32,000,000

            0.625 g                                                 48,000,000

Interpolate to obtain the time at 1 gram;

1.25 g ----------------------------------   32,000,000

1 g --------------------------------------------- x

0.625 g --------------------------------------- 48,000,000

[tex]\frac{1.25 - 1}{1.25 - 0.625} = \frac{32,000,000 - x}{32,000,000 - 48,000,000} \\\\\frac{0.25}{0.625} = \frac{32,000,000 - x}{-16,000,000} \\\\-4,000,000= 20,000,000 - 0.625x\\\\0.625x = 20,000,000 + 4,000,000\\\\0.625x = 24,000,000\\\\x = \frac{24,000,000}{0.625} \\\\x = 38,400,000[/tex]

Therefore, the time taken for the element to remain 1 gram is 38,400,000 unit.

         

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