Question

256gm of a radioactive substance decreases to 2gm in 400days. what is half life of radioactive aubstance​

Answer 1

Radioactive decay is an exponential decay process. [See graph below (personal app)].

The equation governing the graph is: M = [M (0)] e^(- k t) where (e) is the natural base) and (k) is the decay constant.

M (0) = 64 g and M = 2 g. Plug in we obtain: (1/32) = e^(- k 20)

Taking NATURAL LOG of both sides: - 3.47 = - k (20) → k = 0.173

Now let’s bring in the half-life and repeat the process:

(1/2) = e^(- 0.173 t) and taking natural log of both sides: → - 0.693 = - 0.173 t

t = 4 days. Therefore half-life = 4 days.

CHECK: after 4 d there is 32 g left, after another 4, there is 16, another 4, 8 and another 4, 4, and another 4, 2 g left.