Question

A rubidium isotope has a half-life of almost 50 billion years. Given that scientists estimate Earth's age to be 4.6 billion years, what is the most likely percentage of parent to daughter isotopes of this element currently existing on Earth?

Answer 1

Same procedure as before.

Answer 2

This asks for the percentage.
A. Less than 10 percent
B. 25 percent
C. 50 percent
D. More than 75 percent

Answer 3

Yea yea. Still the same as before:
So we are interested in the following:
\[\LARGE N(t)=xN _{0}\]
where x is the percentage:
\[\LARGE x N_{0}=N _{0}e ^{-\lambda*t}\]
Try rewrite so we get an expression for the percentage with the time and half life.

Answer 4

So would it be A. Less than 10 percent
I know with certainty that it is not C or D

Answer 5

Sure?
Think about it... every time there go 50 billion years 50% of the rubidium is gone.

Answer 6

But the earth it self is not 50 billion years.

Answer 7

lets try calculate it:
\[\LARGE x=e ^{- \lambda*t}\]
\[\LARGE x=e ^{-\frac{ \ln(2) }{ t _{1/2} }*t}\]
This is our expression as we have all the known variables:
\[\LARGE x=e ^{-\frac{ \ln(2) }{ 50*10^{9} years }*4.6*10^{9} years}=0.9382211965\]

Answer 8

Then its D.

Answer 9

Exactly. we know automatically it can't be A, B or C just by looking at the half life... for the C option to be right then the half life need to equal the earth's life time... but since half life >> earth life time then we know the procentage > 50%

Answer 10

Oh I get it now!! Thank you, Frostbite!!

Answer 11

Glad I could help.

Answer 12

And thank you for the medal.

Answer 13

: o )