Question

According to the data in the chart, what is the approximate half-life of each element? (HELP! SEE ATTACHMENT)

Answer 1

what are they in column A,B,C,D,E?

Answer 2

can't see what each column represents...

Answer 3

Sorry, about that .. Those columns are the elements . Elements A, B, C, D, E.

Answer 4

Column A is the year

Answer 5

Use the relation \[N=N _{0}e ^{-\lambda t}\] where N is number of atoms remaining after time t
N0 is initial number of atoms
lambda=0.693/(half life), is disintegration constant
t is time

you can form a lot of equations for each element and solve to get value of half life..

Answer 6

Can you do one example for me so I can understand it better?

Answer 7

let the initial number of atoms for element A be N1
Now, after 1000 (years, months or seconds whatever is the unit of time),
\[90=N _{1}e ^{(-0.693/T _{1/2})1000}\]
In the similar way replace 90 with 73 and t with 3000
you will get another equation
solve those two
you will get T1/2 (i.e. half life)

Answer 8

Thank you.

Answer 9

welcome.. :)

Answer 10

So if i were to find the half life of Purple, I would do 50 and 13 with 3,000?

Answer 11

is that purple? that seems a bit yellowish to me...
well, yes, follow the same process for all elements..

Answer 12

Last question: How much of the parent isotope remained after two half-lives?

Answer 13

Colum C is 1000

Answer 14

\[\frac 12 \times \frac 12=\frac 14\]
quarter of the original, after 2 half lives

Answer 15

After 1 half life atoms disintegrated= 1/2 of initial atoms
After two half lives,
the number of atoms disintegrated= 1/2 of initial atoms + 1/2 of atoms remaining after one half life
=1/2 of initial atoms + 1/4 of initial atoms =3/4 of initial atoms

so, after two half lives atoms remaining=1-3/4=1/4 of initial atoms

Alternative process,
we have a relation, fraction of atoms remaining after n half lives=(1/2)^n
here n=2
so, fraction of atoms remaining after two half lives= (1/2)^2 =1/4 of initial atoms