1. ## Half Life Question

The radioactive isotope uranium-232 has a half-life of 68.9 years.

The decay constant of uranium-232 is

If you have 35 grams of uranium-232 to begin with, the equation that describes the radioactive decay is

2. By definition 'half time' is the time in which a mass of material subject to decay [Uranium for example...] is halved. The decay law is then...

$\displaystyle m(t)=m_{0}\cdot 2^{- \frac{t}{t_{h}}}$

... where $\displaystyle t_{h}$ is the 'half time' and $\displaystyle m_{0}$ the mass of material at the time $\displaystyle t=0$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Originally Posted by v3ndetta
The radioactive isotope uranium-232 has a half-life of 68.9 years.

The decay constant of uranium-232 is
Recall that $\displaystyle T_{1/2}=\lambda=\frac{\ln 2}{k}$ where $\displaystyle T_{1/2}$ (interchangeable with $\displaystyle \lambda$) is the half life, and $\displaystyle k$ is the decay constant. Thus, $\displaystyle k=\frac{\ln 2}{68.9}\approx\boxed{.0101}$

If you have 35 grams of uranium-232 to begin with, the equation that describes the radioactive decay is

Now that we have $\displaystyle k$, we can set up our equation.
The decay equation has the form $\displaystyle y=y_0e^{-kt}$, where $\displaystyle y_0$ is the initial amount of the substance.
Thus, our decay equation is $\displaystyle \boxed{y=35e^{-.0101t}}$