Question

The cadmium isotope 109Cd has a half-life of 462 days. A sample begins with 1.0×1012109Cdatoms.

a.How many 109Cd atoms are left in the sample after 59 days?

b. How many 109Cd atoms are left in the sample after 220 days?

c.How many 109Cd atoms are left in the sample after 5200 days?

Answer 1

Half-life of 109-Cd = T_1/2 = 462 days

Decay constant =

= 1.5 x 10^-3 days^-1

Initial amount of atoms in the sample = N₀ = 1 x 10¹² atoms

Atoms left in the sample after 59 days = N₁

T₁ = 59 days

N₁ = 9.15 x 10¹¹ atoms

Atoms left in the sample after 220 days = N₂

T₂ = 220 days

N₂ = 7.19 x 10¹¹ atoms

Atoms left in the sample after 5200 days = N₃

T₃ = 5200 days

N₃ = 4.1 x 10⁸ atoms

a) Number of atoms of 109-Cd left after 59 days = 9.15 x 10¹¹ atoms

b) Number of atoms of 109-Cd left after 220 days = 7.19 x 10¹¹ atoms

c) Number of atoms of 109-Cd left after 5200 days = 4.1 x 10⁸ atoms