- #1
Jimmy87
- 686
- 17
Hi,
I was trying to see where the equation N = No e-λt came from and it is derived from dN/dt = -λN which is discussed very well in this thread in post #2 (https://www.physicsforums.com/threads/derivations-of-the-decay-constant-equation.213312/). I understand the steps except for the reason why both sides are integrated. I always struggle with this concept during derivations. If we rearrange it into the form dN/N = - λdt, I really don't see how the next logical step is to integrate both sides. I know it gets us the correct outcome but what is the reason for integrating both sides as appose to some other operation? Integrating means summing/adding - I don't see how summing/adding is the next logical step - I only understand it retrospectively from the correct outcome it gives.
Any help is much appreciated!
I was trying to see where the equation N = No e-λt came from and it is derived from dN/dt = -λN which is discussed very well in this thread in post #2 (https://www.physicsforums.com/threads/derivations-of-the-decay-constant-equation.213312/). I understand the steps except for the reason why both sides are integrated. I always struggle with this concept during derivations. If we rearrange it into the form dN/N = - λdt, I really don't see how the next logical step is to integrate both sides. I know it gets us the correct outcome but what is the reason for integrating both sides as appose to some other operation? Integrating means summing/adding - I don't see how summing/adding is the next logical step - I only understand it retrospectively from the correct outcome it gives.
Any help is much appreciated!