Question

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

Answer 1

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