Hello,I'm revising half-life for GCSE and have come across some

[Molly1235]

Hello,
I'm revising half-life for GCSE and have come across some questions regarding fractions.

For example, "what fraction of the original nuclei will still be unstable after 5 half-lives?"

Am I right in thinking it would be 1/20 as 1/2 x 5 = 1/20 or is that too simple?

Thanks,
Molly

 

[SammyS]

Hello,
I'm revising half-life for GCSE and have come across some questions regarding fractions.

For example, "what fraction of the original nuclei will still be unstable after 5 half-lives?"

Am I right in thinking it would be 1/20 as 1/2 x 5 = 1/20 or is that too simple?

Thanks,
Molly

Yes, that's too simple ... and how is (1/2) × 5 = 1/20 ?

Think about it.

After a time of one half-life, 1/2 of the original nuclei remain unchanged.After a time of an additional half-life, 1/2 of that 1/2 of the original nuclei remain unchanged. This is a total time of two half-lives and 1/4 of the original nuclei remain unchanged.

Etc.

 

[Molly1235]

Yeah, thank you I just realized I was being stupid. It's 1/32 right?

 

[SammyS]

Yeah, thank you I just realized I was being stupid. It's 1/32 right?

Right ! I mean, right, it's 1/32, not right about the other thing!

 

[Nickie]

Hello Molly,

You are correct in thinking that after 5 half-lives, 1/20 of the original nuclei will still be unstable. This is because for each half-life, half of the original nuclei decay, leaving half still remaining. So after 5 half-lives, we can calculate it as 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32, which is very close to 1/20. It is important to keep in mind that the fraction of unstable nuclei decreases exponentially with each half-life, so the remaining fraction becomes smaller and smaller. I hope this helps with your revision. Good luck!