Question

A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 86.8 y?

Answer 1

STEPS : 1- WE NEED TO CALCULATE DECAY CONSTANT λ

2- WITH λ WE CAN CALCULATE REAMING RADIOACTIVE MATERIAL  

FORMULA: half-life t_1/2=ln2 /λ (λ is the decay constant )

so λ=ln2/t_1/2 (t_1/2 given = 30.7 years)

λ= 0.693/30.7 = 0.02257

NOW N_t = N₀e^−λt

N₀ is the initial quantity

N_t   is the remaining quantity after time, t
t_1/2 is the half-life
t time (given 86.8year)
λ is the decay constant

  N_t /N₀=e^−λt

  N_t /N₀=e^{−(.02257 X 86.8)}

N_t /N₀=e^{−(.02257 X 86.8)}

N_t /N₀=0.140

N_t =0.1410 No

14.10 % will remain after 86.6 years.