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Half life

1) Radioisotopes such as aluminum -26, which is believed to have been present in the solar system when earth was formed but can no longer be detected, are known as extinct radionuclides. The half-life for the decay of aluminum -26 is 7.20 x 10 ^5 years.
How many years did it take for 99.99% of the aluminum -26 to decay? If Earth was formed 4.6 x10^9 years ago, what percentage of the aluminum-26 present when the solar system was formed is still present today?

Solution Preview

N(t)= N(0) exp (-lambda t)
where
N(t)= Amount at time t
N(0)= Amount at time 0
lambda = decay constant
t= time elapsed

half life=T( 1/2)= 7.20 x 10 ^5 years.= 720000 years

lambda =ln 2 / T( 1/2)= 9.627E-07 =0.693147/720000
or 9.627 x 10 ^ -7 years ^ -1

How many years did it take for 99.99% of the aluminum -26 to decay?

N(t)= N(0) exp (-lambda t)
or t= ln [N(0)/N(t)] / lambda

for 99.99% of the aluminum -26 to ...

Solution Summary

The solution calculates the number of years it takes for 99.99% of the aluminum -26 to decay.

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