# How do you find the half life of uranium-235? I tried to do 235 / 2 = 117.5 but that is wrong please help

## half life is when you half/divide a number by 2 does this necessary mean that you divide or do you have to work out something else before dividing?

Mar 23, 2017

#### Explanation:

To find the half-life of any radioactive substance, you need to start with an initial mass of the substance, $Q \left(0\right)$, then, after a time interval ,t, you carefully measure the mass of the substance, Q(t)

$Q \left(t\right) = Q \left(0\right) {e}^{\lambda t}$

Both $Q \left(0\right) \mathmr{and} Q \left(t\right)$ are in the same units of mass so this means that the exponential us unit-less (as it should be)

Let's solve for $\lambda$.

$\frac{Q \left(t\right)}{Q \left(0\right)} = {e}^{\lambda t}$

$\ln \left(\frac{Q \left(t\right)}{Q \left(0\right)}\right) = \lambda t$

$\lambda = \ln \frac{\frac{Q \left(t\right)}{Q \left(0\right)}}{t}$

Please notice that $\lambda$ must be in ${\text{time units}}^{-} 1$, because t is in time units.

Now suppose that you are given a value for $\lambda$ and you want to know the time, ${t}_{\text{half-life}}$. (Which is defined as the time that it takes for half of the original quantity to decay.)

(Q(t_"half-life"))/(Q(0))= e^(lambdat_"half-life")

We know that the left side is $\frac{1}{2}$

$\frac{1}{2} = {e}^{\lambda {t}_{\text{half-life}}}$

$\ln \left(\frac{1}{2}\right) = \lambda {t}_{\text{half-life}}$

$- \ln \left(2\right) = \lambda {t}_{\text{half-life}}$

${t}_{\text{half-life}} = - \ln \frac{2}{\lambda}$

Suppose that you are given the half-life and you need to find $\lambda$

$\lambda = - \ln \frac{2}{t} _ \text{half-life}$

The half-life for ${U}_{235}$ is $7.04 \times {10}^{8} \text{ years}$

For ${U}_{235}$, $\lambda = - 9.84 \times {10}^{-} 10 {\text{ years}}^{-} 1$