The Isotope calcium-41 decays Into potassium-41, with a half-life of 1.03 x 105 years. There is a sample of calcium-41 containing 5 x 10⁹ atoms.How many atoms of calcium-41 and potassium-41 will there be after 4.12 x 105 years?
OA 3.125 x 108 atoms of calcium-41 and 4.375 x 10⁹ atoms of potassium-41
OB. 6.25 x 108 atoms of calcium-41 and 4.6875 x 10° atoms of potassium-41
OC. 6.25 x 108 atoms of calcium-41 and 4.375 x 109 atoms of potassium-41
OD. 3.125 x 108 atoms of calcium-41 and 4.6875 x 10° atoms of potassium-41
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The correct answer for this question will be option D.
Calcium-41 = 3.12× atoms
Potassium-41 = 4.69× atoms
As stated in the question,
Half life of isotope of Ca-14 which decays into K-14 = 1.03 × years
Therefore, after 1.03 × years (1 half life)
Ca-41 will be 50%
and, K-41 will be 50%
After 2.06 × years (2 half lives)
Ca-41 will be 25%
K-41 will be 75%
After 3.09 × years (3 half lives)
Ca-41 will be 12.5%
K-41 will be 87.5%
After 4.12 × years (4 half lives)
Ca-41 will be 6.25%
K-41 will be 93.75%
After 4.12 × years,
Ca-41 = 6.25/100 × 5×
= 3.12 × atoms
K-41 = 93.75/100 × 5×
= 4.69 × atoms
Therefore, option D is correct.
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