A 100 gram sample of radium-226 has a half life of 1,600 years. how long will it take before before there are only 12.5 grams of the radioactive radium-226 remaining

Radioactivity is studied very well by scientists that they have established a pseudo-first order reaction for this process. The working equation for this problem is:

h = ln 2/k

where

h is the half-life

k is the reaction constant

1600 = ln2/k

k = 4.33*10⁻⁴/yr

Then, we use

A = A₀e^ (-kt)

A is the amount left after time t

A₀ is the original amount

t is the time

12.5 = 100e (-4.33*10⁻⁴*t)

t = 4,800 years