Question

Jacobium is a radioactive metal with half life of 20 years. It contains 128 radioactive atoms. How many years will it take to decay to 2 radioactive atoms

Answer 1

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
`e^(-\lambda t)`

inserting the values

2 = (128)
`e^(-(0.0347) t)`

t = 120 years