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rhettperkins
12.02.2022 •
Mathematics
The height of a plant was measured after it
was planted measured in months, t, as
shown in the table What was the initial height
of the plant when it was planted?
T H
1 21
2.5 28.5
5. 41
Solved
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Ответ:
Decay equation is given by
where A is amount at time t, P is original amount, k is decay constant, t is time
So using this on isotope A first. It decays to 10% of original. So lets say its original amount was
, so now its amount will be 10% of
which will be ![0.1P_{1}](/tpl/images/0114/1510/60fbe.png)
So plug
in A place,
in P place, then 33 as time in t place and let its decay constant be
. So plug all these in equation (1)
Divide both sides by![P_{1}](/tpl/images/0114/1510/03ad6.png)
Solve for![k_{1}](/tpl/images/0114/1510/b20f9.png)
for that take ln on both sides
Similarly for isotope B, if its original amount was
then 10 % of
will be
. And if its decay constant be
and its time is 43
so plug these in equation (1)
Divide both sides by![P_{2}](/tpl/images/0114/1510/22d1b.png)
again solve for![k_{2}](/tpl/images/0114/1510/d35b4.png)
Now half life means amount is 1/2 of original amount. So that means if P is original amount then A will become
or 0.5P
Using this in equation (1) we get
Divide both sides by P
thats the equation for half life
So plug result of
as -0.069775 in k place in equation (4) we get its half life as
So life for isotope A is 9.933989
Similarly find half life of isotope B.
For that plug
as -0.053548 in k place in equation (4) we get its half life as
so half life of isotope B is 12.9443
Now find difference betwen half lives of two isotopes by subtracting results (5) and (6)
so we get final answer as 12.9443- 9.933989 = 3.01
So choice A as 3 is the right answer.