nuclear decay

Daniel123 · 2007-10-08 08:09:09

How do I find what t is?

Does anyone mind explaining how to do it? I haven't done it in maths yet.

Thanks.

luca-deltodesco · 2007-10-08 09:02:26

the operation your looking for is the logarithm - in this case the natural logarithm (logarithm base e)

logarithm is the inverse operation of exponential. i.e.

for example:

i say in the reals, because in the complex numbers, logarithm is non unique, but you can be assured that for all real x and a this will hold

so in otherwords:

you can work out the right hand side on a calculator, and then divide by the coefficient of 't' to get the value of 't'

note that

going from original equation:

Last edited by luca-deltodesco (2007-10-08 09:07:46)

Daniel123 · 2007-10-08 09:08:46

Aah right, not too difficult.

Thanks luca

luca-deltodesco · 2007-10-08 09:14:36

also, realise that working it out using my last formula in terms of N and lambda will give more accurate results when computed using either a computer or a calculator as you are dealing with large numbers instead of very small numbers, and logarithm's are better approximated with large rather than small numbers.

working it out with your rearrangement i get:
2738274191766.0933
which when plugged into first equation will give a difference in values of :
1620000000

whereas using direct rearrangement for t in terms of N and lambda with two logarithms gives
2738396562095.8906
which gives a difference of:
0.0029296875

very different results, but you can see that either would give you a right answer in any question since they aern't going to ask for accuracy beyond 4 significant figures

in other notes, wow thats a long half life, over 86 thousand years o.O

Last edited by luca-deltodesco (2007-10-08 09:17:54)

Math Is Fun Forum

#1 2007-10-08 08:09:09

nuclear decay

#2 2007-10-08 09:02:26

Re: nuclear decay

#3 2007-10-08 09:08:46

Re: nuclear decay

#4 2007-10-08 09:14:36

Re: nuclear decay

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