- #1
sam400
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Homework Statement
Basically, the problem asked for the half life of Thorium-232, given the initial mass and the rate of decay.
\begin{equation}
\frac{dN}{dt} = 4100 \frac{ \alpha }{s}
\end{equation}
initial mass = 1.0 g
Homework Equations
\begin{equation} \frac{dN}{dt} = \lambda N \end{equation}
\begin{equation} t_h = \frac{ \ln 2}{\lambda} \end{equation}
The Attempt at a Solution
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Started off converting the mass into number of particles:
\begin{equation} 1.0 g \frac{1.0 mol}{232 g} 6.022*10^{23} molecule/mol \end{equation}
That gave me N, which was ##2.59*10^{21}## molecules. From that, I guess I could use the first equation to find the decay constant, so I got ##1.58*10^{-18}##
From that, the second equation can be used to obtain a value for the half life, which then gave me the value, but I had to make sure to convert to years next. After using the proper conversion factor, I got a value of ##8.1* 10^{11}## years, which is different from the literature value of 1.4*10^{10}. I have a feeling I shouldn't have done what I did to find the decay constant, but I'm not entirely sure what other approach I can take, since I'm still new to nuclear. Thanks in advance.Edit; I just realized that the method in my original post does give me the value found in literature. However, if I try to do it with a slightly different method, ie. convert the decay rate into grams/second, I seem to be getting the wrong answer.
\begin{equation} 4100 \frac{\alpha}{s} \frac{ 6.64E-27 kg}{ 1 \alpha} \frac{1 g}{10^{-3} kg} = 2.72E-20 g/s \end{equation}
This gives me a different decay constant value entirely, which then gives me the value I originally stated, so I think my original method is still wrong, or I made a conversion error.
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