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.
