SOLUTION: The half-life of a radioactive element is 131days, but your sample will not be useful to you after 70% of the radioactive nuclei originally present have disintegrated. About how ma

Question 451673: The half-life of a radioactive element is 131days, but your sample will not be useful to you after 70% of the radioactive nuclei originally present have disintegrated. About how many days can you use the sample?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The half-life of a radioactive element is 131 days, but your sample will not be
useful to you after 70% of the radioactive nuclei originally present have disintegrated.
About how many days can you use the sample?
:
The radioactive decay equation: A = Ao*2^(-t/h), where
A = resulting amt in t time
Ao = initial amt
t = time
h = half-life of substance
:
Let Ao = 1
the
A = .3 after 131 days (70% decayed)
:
1*2^(-t/131) = .3
ln(2^(-t/131)) = ln(.3)
log equiv of exponents
*ln(2) = ln(.3)
=
= -1.7369656
t = -1.7369656 *-131
t = +227.5 days, the substance is useful
:
;
Check on a calc: enter 2^(-227.5/131) results .300

RELATED QUESTIONS
Q15. The half-life of a radioactive element is 130 days, but your sample will not be... (answered by KMST)

A radioactive chemical element has a half life. This means that after a specific length... (answered by ankor@dixie-net.com)

Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000... (answered by ankor@dixie-net.com)

If 80% of a radioactive element remains radioactive after 200 million years, then... (answered by ikleyn,Theo,greenestamps,josgarithmetic)

If 80% of a radioactive element remains radioactive after 200million years, then what... (answered by Edwin McCravy)

Hi I need help on my homework. Would you kindly please show me how to solve this problem. (answered by josgarithmetic)

Please show step by step. Thanks An unknown radioactive element decays into... (answered by josgarithmetic)

An unknown radioactive element decays into non-radioactive substances. In 820 days the... (answered by Fombitz)

An unknown radioactive element decays into non-radioactive substances. In 560 days the... (answered by josgarithmetic,greenestamps)