In chemical equilibrium, radioactive decay occurs because of unstability due to the high neutron-to-proton ratio. Through time, the radioactive element is converted to a new element. This radioactive decay undergoes first order reaction. Its equation is in the form of
A = A₀e^(-kt), where A is the amount of the element after time t, A₀ is the original amount of element at t=0 and k is the rate constant.
Half-life is the amount of time for A to be 1/2 of A₀. Modifying the equation during half time, we let A=1/2 A₀. Then.
1/2 A₀ = A₀e^(-kt)
1/2 = e^(-k(5730))
k = 0.000121
Thus, the first-order rate constant is equal to 0.000121 per year.