A certain radioactive isotope is a byproduct of some nuclear

^{A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 10 days. Estimate the percentage of the original amount of the isotope released by the explosion that remains 3 days after the explosion.}

Solution

Half life of the isotope = 10 days;
half life is = 0.693/ k where \'k\' is the decay constant;
10 = 0.693/k so k = 0.693/10 = 0.0693;

Thus N = N_o e^-kt

(N_o is the initial quantity of the radiactive material;
N is the quantity of radioactive material left after \'t\' days;
K is the decay constant given by k = 0.693/t_1/2
t_1/2 is the half life of the material which is = 10 days in this case)


but after t=3 days N= N_o e^-0.0693*3 = N₀ 0.8122
Thus N= N₀ (0.8122)
which means after 3 days there will be 81.22% of the original isotope left after the explosion;