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.

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.

My son with the litty explanations

10 minute is correct

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.

Oh, radioactive elements and their half-life shenanigans! Let me explain it to you with a touch of humor.

Imagine you have a radioactive element at a party, and it's feeling a bit shy. So, every 30 minutes, it loses some of its coolness (or radioactive particles) to fit in better.

Now, if it goes from 80mg to 10mg in 30 minutes, that means it has lost 70mg of its coolness.

To figure out the half-life, we need to determine how long it takes for the element to lose half of its original coolness.

If it lost 70mg in 30 minutes, logically it would lose 40mg in 20 minutes (half of 80mg). So, we can conclude that the half-life is 20 minutes, not 10 minutes.

So, the answer should be b. 20 min.

Remember, even in science, you can't always trust numbers. Sometimes, you need a bit of clowning around to make sense of them!

To determine the half-life of a radioactive element, we need to understand the concept of half-life and use the given information.

Half-life is the time it takes for half of a sample of a radioactive substance to decay. In this case, we have 80mg of the substance initially, which decays to 10mg after 30 minutes.

Let's calculate how many half-lives have occurred:

1st half-life: The initial amount is 80mg, and after 30 minutes, it decays to 10mg.

So, after the 1st half-life, we have 10mg remaining.

Since half of the substance decays during each half-life, the second half-life will also result in 10mg / 2 = 5mg remaining.

Given that the initial amount was 80mg and it took 2 half-lives to reach 5mg, we can calculate the half-life as follows:

80mg (initial amount) ÷ 2 (number of half-lives) = 40mg (half-life amount)

Therefore, the half-life of this radioactive element is 40 minutes.

However, the given options for the answer do not include this value. Let's see which option can be considered correct by process of elimination:

Option a: 10 minutes - This is the correct answer.

Option b: 20 minutes - This is not the correct answer.

Option c: 30 minutes - This is not the correct answer.

Option d: 40 minutes - Although this is the calculated half-life, it is not provided as an option, so it is not the correct answer.

Therefore, the correct answer is option a: 10 minutes.