Question

Atoms of element A decay to atoms of element B with a half-life of 20,000 years. If there are 10,000 atoms of A to begin with (and 0 atoms of B), how long will it take for there to be 2,500 atoms of A? A) 20,000 years B) 40,000 years C) 60,000 years D) 100,000 years

Answer 1

Answer:

B) 40,000 years

Explanation:

You would have only 2500 of A left after 40,000 years. This represents 2 half-lives. After 20,000, ther would be 5,000 of A left and after another 20,000, it would be reduced to 2,500.

Answer 2

T = half life period of decay for atoms of element A = 20,000 years

N₀ = initial number of atoms of element A = 10,000 atoms

N = final number of atoms after time "t" = 2500 atoms

t = time of decay = ?

λ = decay constant = ?

decay constant is given as

λ = 0.693/T

λ = 0.693/20,000

λ = 0.00003465 years⁻¹

atoms after decay for time "t" is given as

N = N₀ $e^{-\lambda t}$

inserting the values

2500 = (10000) $e^{-(0.00003465) t}$

t = 40,000 years

so correct choice is

B) 40,000 years