Register to reply 
Radioactive decay formula 
Share this thread: 
#1
Jun508, 03:49 PM

P: 5

What lead them to use e and the natural log of 2 in the decay formula? A much simpler (to me at least) method would is:
N=No*.5^(time/half life) 


#2
Jun508, 07:26 PM

HW Helper
P: 6,208

Well since
[tex]N=N_0 e^{ \lambda t}[/tex] when t=halflife(T); N=[itex]\frac{N_0}{2}[/itex] [tex]\frac{N_0}{2}=N_0 e^{ \lambda T}[/tex] simplify that by canceling the N_0 and then take logs and you'll eventually get [tex]T=\frac{ln2}{\lambda}[/tex] 


#3
Jun508, 07:48 PM

P: 5




#4
Jun508, 09:40 PM

Mentor
P: 16,111

Radioactive decay formula
It's the same question as "why log base e and not log base 2"? It happens to make some calculations easier. (Note that your calculator has a ln(x) button but probably not a log2(x) button)



#5
Jun508, 09:51 PM

P: 5

It could also be I use it just to make my teacher grade things two ways xD 


#6
Jun608, 02:51 AM

Sci Advisor
HW Helper
P: 4,739

the differential equation is:
[tex] \frac{dN}{dt} = \lambda N [/tex] Solve it. 


#7
Jun608, 07:36 AM

P: 5

I believe you have to use integrals to solve that, which I haven't done yet. 


#8
Jun608, 07:58 AM

Sci Advisor
HW Helper
P: 4,739

Solving this: [tex] \int N ^{1}dN =  \int \lambda dt [/tex] [tex] \ln(N(t))  \ln(N(0)) = \lambda t [/tex] [tex] \ln(N(t)/N(0)) = \lambda t [/tex] [tex] N(t)/N(0) = e^{\lambda t } [/tex] [tex] N(t) = N(0) e^{\lambda t } [/tex] Lambda is the number of decays per unit time, is related to half life by: [tex] \lambda = \frac{\ln 2}{T_{1/2}} [/tex] 


#9
Jun608, 08:07 AM

P: 5




#10
Jun608, 08:11 AM

Sci Advisor
HW Helper
P: 4,739

it is easier working with base e when solving the differential eq.
Then if you think it is easier to work in basis 0.5 when you calculate, then it is up to you. 


Register to reply 
Related Discussions  
Radioactive decay  Introductory Physics Homework  1  
What is the proper use and meaning of Radioactive decay ? How much decay HAS occured  General Physics  2  
Radioactive decay equilibrium when decay constants are equal  Biology, Chemistry & Other Homework  2  
Radioactive Decay  Introductory Physics Homework  3  
Radioactive Decay  Calculus  2 