What is the formula when two exponential-decay processes take place simultaneously?

Aug 10, 2014

The formula is N_t = N_0e^-((λ_1 + λ_2)t).

For a single decay mode, the formula for decay rate is

-(dN)/(dt) = λN

If there are two different simultaneous decay processes, the total decay rate is the sum of the two processes.

-(dN)/(dt) = λ_1N + λ_2N = (λ_1 + λ_2)N

On integration, this becomes

N_t = N_0e^-((λ_1 + λ_2)t)

We can simplify this by defining a new total decay constant λ_"c":

λ_"c" = λ_1 + λ_2

Then the equation becomes

N_t = N_0e^-(λ_"c"t)