Am I Stupid ???

[xaris101]

hey, i was trying to solve this problem and i can't although it seems stupid ...can someone help ???


The radioactive element polonium has a half life of 140 days, which means that because of radioactive decay, the amount of polonium remaining after 140 days is one-half of the original amount. Starting with 10 grams of polonium today, determine how much is left after 250 days?




i now that i to find an equation relating the amount left to the initial amount, half-life time and time passed)

[opus]

A formula like:

Remaining= (1- 0.0049388153)^Number of days


The correct value for the "0.0049388....." would be 1-(140th root of 0.5)!

[Glaysher]

y = 10e^-tx

5 = 10e^-140t

0.5 = e^-140t

ln 0.5 = -140t
t = (ln 0.5)/-140

Calculate and use for t in the first line

Then stick in x = 240 to find amount left after 240 days

[xaris101]

you mean 250 days and not 240 ,right ???

[Glaysher]

you mean 250 days and not 240 ,right ???

Yeah, sorry, misread it

[Ember]

Or in shorter form:

A = 1- 0,5^(250/138.4)

where 138,4 is the half life of polonium. But how to find the equivalent dose of 100 times deadly dose is something for experts.

[FireEater]

Hi,


Just for the record. The formulae discussed are based on the hypothesis that the decay is exponential, which, less 'jargonly' amounts to our assuming this:

That the rate of decay is proportional to the amount of substance that has so far not decayed.

Once we are clear on this, the formula can be derived by elementary techniques for solving differential equations.

Lastly, let the record show that this treatment (first order kinetics) is only an approximation. As Einstein had it 'In so far as the equations of physics refer to reality, they are not exact; and in so far as they are exact, they do not refer to reality'


Tataa!