The isotope calcium-41 decays into potassium-41, with a half-life of 1.03 × 10^5 years. there is a sample of calcium-41 containing 5 × 10^9 atoms. how many atoms of calcium-41 and potassium-41 will there be after 4.12 × 10^5 years? how many calcium and how many potassium?

1.) Find The Number of Half Lives Passed:

half lives

2.) Calculate Number of Ca Atoms remaining:

atoms left

3. Calculate Number of Potassium Atoms

Subtract the final number of Calcium atoms from the initial amount of calcium atoms.

Atoms of Potassium

Draw a diagram to illustrate the problem as shown below.

Calculate the volume of the empty cone.
V₁ = (1/3)π*(6 in)²*(10 in) = 120π in³

Calculate the volume of the sphere.
V₂ = (4/3)π*(1.5 in)³ = 4.5π in³

The volume that can be filled with flavored ice is 
V = V₁ - V₂ = 115.5π in³ = 362.85 in³

Th volume is 115.5π in³ or 362.9 in³ (nearest tenth)