I am NOT smarter than an 8th grader! (Chemistry homework help).

[PrincessParty]

For the love on Pete (our cat who is keeping me company as I try to figure this problem out) I am overlooking the obvious:

Determine the half-life of a radioactive substance that has changed through radioactive decay. After 40 days, the original substance left is one-sixteenth of the original amount.

Is it 160?

1-1/2-1/4-1/8-1/16

Thanks to anyone having brain cells that actually synapse at this hour.

 

[kinntj]

my dh said it's 4 cyles, so 10. Someone else might be able to verify that.
That's math. you should be dividing not multiplying.

 

[clh2]

I came up with 5 days for the half life. Can't explain it other than:

40 days =1/16
20 days =1/8
10 days =1/4
5 days =1/2

I just worked backwards.

YIKES - I did it wrong...it is 10 days...

There is actually a calculator here:

In this case - the time = 40days, the beginning amount would be 1 and the ending amount would be 1/16th.

 

[kinntj]

I came up with 5 days for the half life. Can't explain it other than:

40 days =1/16
20 days =1/8
10 days =1/4
5 days =1/2

I just worked backwards.

that makes more sense.

 

[PrincessParty]

Thank you guys, it has been MANY years since I took chemistry and I just can't do basic math at this hour. Just didn't seem like enough info for the problem.

Thanks again.

 

[locolala]

If the particle is at 1/16th after 40 days, then the half life is 10 days.

 

[AbbysFamily]

Sorry clh2.... kinntj's DH is right...
If you take clh2 answer of 5 days....
5 days = 1/2
10 days = 1/4
15 days = 1/8
20 days = 1/16 .... This doesn't match the 40 days stated.

however
10 days = 1/2
20 days = 1/4
30 days = 1/8
40 days = 1/16

So that matches up with kinntjs answer of 4 cycles... 10 days each... the number of days with each 1/2 life must be constant.

The key here is 1/16 is 1/4 divided by 4... thus 4 cycles... 40 days total with equal days -> 40/4 = 10.

 

[clh2]

Sorry for the bad info above - 10 days is correct.

Darned homework...


I'm trying to think too logically...

If you start with 1
you will have 1/2 after 10 days
then you will have 1/4 after 20 days
then you will have 1/8 after 30 days
and you will have 1/16th left after 40 days.

OK - at least I realized where I screwed up!

 

[PrincessParty]

DD took 40 being the ending and multiplied up 4 cycles to 160 instead of dividing. Thank you all for your help. She is a straight A honor's student, and this is the first day of the new semester, and she is really stressed tonight over this. I knew you all could help. Thanks!

 

[The Mystery Machine]

I can't do my 7th graders algebra. I feel your pain.

 

[kinntj]

Thankyou for verifying that. I told him 5 and he said no, it's 10. I just left it, because I wasn't sure myself and DH was going to bed and getting grumpy with me.
OP I'm glad that you got the answer verified for your DD. That's great she's taking chemistry in 8th grade. I took it in college and it's hard to retain all that information over the years.

My teacher always showed 1/2 lives set up as a grid (think tic tac toe)to figure out time or amount.

Sorry clh2.... kinntj's DH is right...
If you take clh2 answer of 5 days....
5 days = 1/2
10 days = 1/4
15 days = 1/8
20 days = 1/16 .... This doesn't match the 40 days stated.

however
10 days = 1/2
20 days = 1/4
30 days = 1/8
40 days = 1/16

So that matches up with kinntjs answer of 4 cycles... 10 days each... the number of days with each 1/2 life must be constant.




The key here is 1/16 is 1/4 divided by 4... thus 4 cycles... 40 days total with equal days -> 40/4 = 10.

 

[PrincessParty]

Thank you all again. It was the first day of doing half life for her and she had 5 problems for homework. That one didn't have as much info as the others so she couldn't use the formula to cross multiply as she did for the other problems. (Which is why she multiplied up 4 cycles.) It was just a feeling she had that 160 wasn't right. I'm anxious for her to get her paper back, but I am sure the Dis earned an A+, with bonus points for having brain power so late.

Her school system does honor's classes in junior high with the option of general, college prep, honor's, or advanced placement classes in high school.

Thanks again.

 

[Darsa]

Ewwww, math...

Do what I always do: "Go ask your father!" (I have always been horrible at math)

 

[paintnolish]

My 4th grader's math makes my brain hurt. What can I say...I am an English major for a reason!

 

[PrincessParty]

What can I say you guys were right!?!

However, DD says a huge "thank you" as a hot guy in her class asked her what she got for that answer and how she got it.

I however am .

Thank you from both of us. (3 if we include hot guy who has never talked to her before today.)

DD thinks the Dis rocks! We already knew it did.

No chemistry homework tonight as it was lab day.