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

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

inserting the values

2500 = (10000)

t = 40,000 years

so correct choice is

B) 40,000 years

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