# Chemistry

IF 80mg of a radioactive element decays to 10mg in 30 minutes, the half-life of this element is
a.10 min
b.20 min
c.30 min
d.40 min

the answer is a.10 min but i would like to know why, please help.

1. 👍 1
2. 👎 0
3. 👁 457
1. ln(No/N) = kt
No = 80 mg
N = 10 mg
t = 30 min
solve for k, then
k = 0.693/t1/2
Substitute k from above and solve for t1/2
10 min is correct.

1. 👍 0
2. 👎 0
2. 10 minute is correct

1. 👍 0
2. 👎 0
posted by shemelis
3. The person asking the question is asking why ? s/he did not challenge the answer 10min. But most respond just show how to get the answer and did not answer the why .. So here is my attempt.

I think first off, you need to re-affirm your understanding of the definition of half-life .
Half-life is the time taken for the element to decay to half of its original mass. so if it started off as 80gm at the start ,it reaches it first half-life when the mass is 40gm.

Since it is a MCQ multiple choice question . Let just say we find the answer by elimination . We can start from an answer we might think is most likely wrong .. For me I will try (c).

Consider (c. 30min). If this answer is true, the sample ought to reduce from 80gm to 40gm after 30min. but the question says that it is already left with 10gm after only 30 min. So (c) 30min, is quickly recognizable as a wrong answer.

if you tried to do (d) and (b) you should get similar conclusion .

Now I skipped to (a) to try.

Consider (a. 10min). if it this half-life. The sample, ought to reduce from 80gm to 40gm after 10min. And then from 40gm to 20gm in the next 10min. And then from 20gm to 10gm after another 10min. So all in all, from 80gm to 10gm in 30min. This seems consistent the original description of how it was observed to have behaved.

Note that if you have got the definition of half-life wrong, you would not recognize (a) as the correct answer.

This question is not so much a test of mathematics skill. More a test of the concept and definition.

If they really want to be confusing they can set the questions as...
"IF 80.8991234gm of a radioactive element decays to 10.12389gm in 30.1284938 minutes, the half-life of this element is ".... . But they didn't. They made the mathematics very very very simple.

1. 👍 2
2. 👎 0
posted by TJ
4. My son with the litty explanations

1. 👍 1
2. 👎 0

## Similar Questions

1. ### chemistry

If there are 80 milligrams of a radioactive element decays to 10 milligrams in 30 minutes then what is the elements half life in minutes? Ok i narrowed it down to either 10 or 30...but im rly confused so if u could help it wuld be

asked by jojo on March 4, 2007
2. ### PRe calc story problem!!

A radioactive element decays exponentially according to the function Q(t) = Q0ekt .If 100 mg of the element decays to 25 mg in 12 days, find the half-life of the element.

asked by Rania on March 10, 2017
3. ### pre calc

A radioactive element decays exponentially according to the function Q(t) = Q0ekt .If 100 mg of the element decays to 25 mg in 12 days, find the half-life of the element. please help

asked by Rania on March 10, 2017
4. ### math

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain? Begin amount is 1.0 elapsed time is 90y half life 30 years n=9/30 n=3 90/2^2 90/8 =

asked by Lynette on March 24, 2017
5. ### Science

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain? Begin amount is 1.0 elapsed time is 90y half life 30 years n=9/30 n=3 90/2^2 90/8 =

asked by Lynette on March 24, 2017
6. ### math

An unknown radioactive element decays into non-radioactive substances. In 100 days the radioactivity of a sample decreases by 64 percent. a)(a) What is the half-life of the element? half-life: b)How long will it take for a sample

asked by Rachel on May 18, 2013
7. ### Engineering Math

An unknown radioactive element decays into non-radioactive substances. In 120 days the radioactivity of a sample decreases by 59 percent. What is the half life of the element? How long will it take for a sample of 100 mg to decay

asked by Erica on September 23, 2016
8. ### Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent. 1.What is the half-life of the element? 2.How long will it take for a sample of 100 mg to

asked by Kim on March 6, 2009
9. ### Pre calc

If 250 mg of a radioactive element decays to 200 mg in 48 hours, find the half-life of the element

asked by Dom on April 28, 2010
10. ### college algebra

In 4 years, 30% of a radioactive element decays. Find its half-life. (Round your answer to one decimal place.) _____ yr

asked by Dee on November 17, 2013

More Similar Questions