If you have 128 atoms of a radioactive substance, with a half-life of 31 seconds, how many atoms would remain after 62 seconds? Please show your work.

N = 32 atoms

Explanation:

The radioactive elements decays as follows:

Ln (N/N₀) = -kt

Where N are number of atoms after t time, N₀ are initial number of atoms, k is decay constant in time⁻¹

We can obtain k from t(1/2):

k = ln 2 / t(1/2)

k = 0.02236s⁻¹

Ln (N/128 atoms) = -0.02236s⁻¹*62s

(N/128 atoms) = e^-1.386

N/128 atoms = 0.25

N = 128 atoms * 0.25