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

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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?

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Answer 1 · 2017-03-23T22:27:45

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, $Q (0)$ $Q(0)$ , 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:

$Q (t) = Q (0) e^{λ t}$ $Q(t) = Q(0)e^(lambdat)$

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

Let's solve for $λ$ $lambda$ .

$\frac{Q (t)}{Q (0)} = e^{λ t}$ $(Q(t))/(Q(0))= e^(lambdat)$

$ln (\frac{Q (t)}{Q (0)}) = λ t$ $ln((Q(t))/(Q(0)))= lambdat$

$λ = \frac{ln (\frac{Q (t)}{Q (0)})}{t}$ $lambda = ln((Q(t))/(Q(0)))/t$

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

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

$\frac{Q (t_{half-life})}{Q (0)} = e_{half-life}^{λ t_{half-life}}$ $(Q(t_"half-life"))/(Q(0))= e^(lambdat_"half-life")$

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

$\frac{1}{2} = e_{half-life}^{λ t_{half-life}}$ $1/2= e^(lambdat_"half-life")$

$ln (\frac{1}{2}) = λ t_{half-life}$ $ln(1/2) = lambdat_"half-life"$

$- ln (2) = λ t_{half-life}$ $-ln(2) = lambdat_"half-life"$

$t_{half-life} = - \frac{ln (2)}{λ}$ $t_"half-life"= -ln(2)/lambda$

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

$λ = - \frac{ln (2)}{t_{half-life}}$ $lambda = -ln(2)/t_"half-life"$

The half-life for $U_{235}$ $U_235$ is $7.04 \times 10^{8} years$ $7.04xx10^8" years"$

For $U_{235}$ $U_235$ , $λ = - 9.84 \times 10^{- 10} {years}^{- 1}$ $lambda = -9.84xx10^-10" years"^-1$

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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?

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Explanation:

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