Question

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?

Answer 1

Please see the explanation.

Explanation:

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

The decay of radio active substances follow this equation:

`Q(t) = Q(0)e^(lambdat)`

Both `Q(0) and Q(t)` 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`.

`(Q(t))/(Q(0))= e^(lambdat)`

`ln((Q(t))/(Q(0)))= lambdat`

`lambda = ln((Q(t))/(Q(0)))/t`

Please notice that `lambda` must be in `"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_"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 `1/2`

`1/2= e^(lambdat_"half-life")`

`ln(1/2) = lambdat_"half-life"`

`-ln(2) = lambdat_"half-life"`

`t_"half-life"= -ln(2)/lambda`

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

`lambda = -ln(2)/t_"half-life"`

The half-life for `U_235` is `7.04xx10^8" years"`

For `U_235`, `lambda = -9.84xx10^-10" years"^-1`