# Calculating ln in radioactive decay

1. Feb 10, 2013

### kjevans

1. The problem statement, all variables and given/known data

N = N0e-λt

N can also be used to describe count rate after a time, (t) where N0 is intial count rate and λ is decay constant.....

Half life, t1/2 od radioactive isotope is

t1/2 = 1n2
λ

The λ should be under the ln2 but it won't let me underneath

How do I calculate 1n??

For example if time (t) in minutes is 10 and Count rate in 1 minute (N) is 82 what is 1n

I dont understand at all? Any helps is grealty appreciated

Thanks

2. Relevant equations

As above

3. The attempt at a solution

I found ln on the calculator but confused how I get the answer from t as and n......

I am doing as biology degree but doing a physics module which I am struggling with

2. Feb 10, 2013

### tms

The equation for decay is
$$N = N_0 \,e^{-\lambda t}.$$
To find the half-life, set $N = N_0/2$:
\begin{align} \frac{N_0}{2} &= N_0 \,e^{-\lambda t} \\ \frac{1}{2} &= e^{-\lambda t}. \end{align}
Now you just solve for $t$:
\begin{align} \ln \frac{1}{2} &= -\lambda t \\ t &= - \frac{1}{\lambda} \ln \frac{1}{2}. \end{align}