N₀ = number of radioactive atoms initially present = 128
N = number of radioactive atoms left after time "t" = 2
t = time taken
T = half life period for the radioactive metal = 20 years
λ = decay constant = ?
decay constant is given as
λ = 0.693/T
inserting the values
λ = 0.693/20
λ = 0.0347
number of radioactive atoms left after time "t" is given as
N = N₀ [tex]e^{-\lambda t}[/tex]
inserting the values
2 = (128) [tex]e^{-(0.0347) t}[/tex]
t = 120 years
