HALF LIFE QUESTION ( Chemistryyy)?

Question

Strontium90has a half life os 28 years, how long will it take for all of strontium 90 presently on Earth to be reduced to 1/32nd of its present amount

Could you explain how to do this question and is the answer 140>?

Answer 1

I'm not going to do your homework for you, but you can do this one in your head.

"The half-life of a quantity subject to exponential decay is the time required for the quantity to decay to half of its initial value."

Meaning that if you have (x) amount of Strontium90 present on earth, after 28 years, you will have 50% of (x) amount remaining. So, after 28 more years, you will have 25% of the initial amount (x) remaining. Just exprapolate the values from there. It's simple math. ;)

Answer 2

at the end of 1 half life, 1/2 of the strontium is present. at the end of two half lifes, 1/2 of 1/2 of the original remails. ie. 1/2 x 1/2. at the end of three half lifes, the remaining is 1/2 x 1/2 x 1/2.

so in general

(1/2) ^ n = amount remaining
where n = number of half lifes that have passed

in your case,

(1/2) ^ n = 1/32
so n = 5

so the time for 5 half lifes to pass is 5 x 28 years = 140 years..

Answer 3

To be reduced to 1/32 of its present amount, it will take 5 half-lives (32 = 2^5; after one half-life, 1/2 of the original amount is left, after 2 half-lives, 1/4 is left, after 3, 1/8, etc.). Thus, the length of time is 5*28 or 140 yrs.

Answer 4

see...
let the present amount be x
after one half life, t , amount left =x/2
second haf lif, 2t, amt left=x/4
..
..
fifth half life, 5t, the amount left=x/32

so time for 5t is == 5*28 == 140..
Hence..