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...

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

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

Kind regards

$\chi$ $\sigma$

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

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

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