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

Paul Duran

Paul Duran

Answered question

2022-05-18

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

Answer & Explanation

rotgelb7kjxw

rotgelb7kjxw

Beginner2022-05-19Added 16 answers

The formula is N t = N 0 e ( ( λ 1 + λ 2 ) t )
For a single decay mode, the formula for decay rate is
d N d t = λ N
If there are two different simultaneous decay processes, the total decay rate is the sum of the two processes.
d N d t = λ 1 N + λ 2 N = ( λ 1 + λ 2 ) N
On integration, this becomes
N t = N 0 e ( ( 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 0 e ( λ c t )

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