The amount of radioactive element that remained after 4 million years has been 50 grams.
The half-life can be defined as the time required by the substance to reduce to half of its initial concentration.
Half-life can be expressed as:
The amount remained after time t = Initial amount [tex]\rm \times\;\dfrac{1}{2}^\frac{t}{Half-life}[/tex]
The half-life for a given radioactive element = 2 million years
The time (t) = 4 million years
The initial concentration = 200 g.
Substituting the values:
The amount remained after 4 million years = 200 g [tex]\rm \times\;\dfrac{1}{2}^\frac{4}{2}[/tex]
The amount remained after 4 million years = 200 [tex]\rm \times\;\dfrac{1}{2}^2[/tex]
The amount remained after 4 million years = 200 × 0.25 g
The amount remained after 4 million years = 50 g.
The amount of radioactive element that remained after 4 million years has been 50 grams.
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