Slope of N - t graph of radioactive decay

Click For Summary
The discussion centers on interpreting the slope of the N versus t graph for radioactive decay, represented by the equation N = N_o e^{-\lambda t}. Participants clarify that while the slope can be easily identified in the log N versus t graph as -λ, the slope in the N versus t graph is not straightforward. The inquiry highlights a need for understanding the relationship between the decay constant and the graph's slope. The conversation also touches on the importance of derivatives in interpreting these graphs. Overall, the main focus is on clarifying the slope's meaning in different graph representations of radioactive decay.
songoku
Messages
2,503
Reaction score
402
Homework Statement
Please see below
Relevant Equations
##N=N_o e^{-\lambda t}##
1713067012655.png


I am not really sure how to interpret the slope. The equation is:

$$N=N_o e^{-\lambda t}$$

If the graph is N against t, then what is the slope?

I can find the slope if the graph is log:
$$log N=log N_o -\lambda t$$

So if the graph is log N against t, then the slope is ##-\lambda##

But if the graph is N against t, I have no idea what the slope is.

Thanks
 
Physics news on Phys.org
Are you familiar with derivatives?
 
Orodruin said:
Are you familiar with derivatives?
Yes. I understand your hint.

Thank you very much Orodruin
 
If have close pipe system with water inside pressurized at P1= 200 000Pa absolute, density 1000kg/m3, wider pipe diameter=2cm, contraction pipe diameter=1.49cm, that is contraction area ratio A1/A2=1.8 a) If water is stationary(pump OFF) and if I drill a hole anywhere at pipe, water will leak out, because pressure(200kPa) inside is higher than atmospheric pressure (101 325Pa). b)If I turn on pump and water start flowing with with v1=10m/s in A1 wider section, from Bernoulli equation I...

Similar threads

Replies
12
Views
1K
  • · Replies 11 ·
Replies
11
Views
6K
  • · Replies 6 ·
Replies
6
Views
8K
  • · Replies 6 ·
Replies
6
Views
907
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 10 ·
Replies
10
Views
1K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K