Understanding Branching Fraction: Ra-226 Example

[leoneul]

I’ve had huge difficulty understanding/interpreting the concept of branching fraction. So correct me if I’m wrong please:
Let’s take the decay of Ra-226 with half-life of 1602 years as an example. It decays through alpha 1 chanel to the excited state of Rn-222 with E=0,187 Mev ( branching fraction 5,4%) and through alpha 2 decay chanel to the ground state of Rn-222 ( Branching fraction 94,6%).

Now my understanding/interpretation :
If we have for example 10^6 Ra-226 nuclides at t=0 , then after 1602 years have passed , 0.054 * ( 10^6 / 2 )=27000 of alpha1 particles and (10^6/2)- 27000=527000 alpah 2 particles will have emitted.

 

[BvU]

Hello leoneul,

Idea's good, math is not : (10^6/2)- 27000=473000

 

[leoneul]

Hello leoneul,

Idea's good, math is not : (10^6/2)- 27000=473000

hehe thanks alot! This simple concept has been causing so much trouble bcs some sources refers to the branching ratio as “ probability” which confused me

 

[mathman]

For anyone atom the branching ratio reflects the probabilities for the channels. Don't overthink!

 

[leoneul]

For anyone atom the branching ratio reflects the probabilities for the channels. Don't overthink!

So for my example the probability that a certain SINGLE Ra-226 nucleus decays through alpha 1 channel is 5.4% but if we have an ENSEMBLE of Ra-226, then 5.4 % will decay through chanel 1. Correct?

 

[BvU]

Again, ideas correct. This time the wording could be a bit sharper by expressing it as a ratio $${\alpha_1\ {\rm decays} \over {\rm total \ decays}} \times 100 \;\%$$ however, litterally taken what you write is correct (but you have to wait infinitely long ...)

 

[leoneul]

Again, ideas correct. This time the wording could be a bit sharper by expressing it as a ratio $${\alpha_1\ {\rm decays} \over {\rm total \ decays}} \times 100 \;\%$$ however, litterally taken what you write is correct (but you have to wait infinitely long ...)

Understood. Thank you very much!