Question

Uranium-232 has a half life of 68.8 years. After 344.0 years, how much uranium-233 will remain from a 100.0-g sample?

Answer 1

Amount of U-232 remaining = 87.06 g

Step-by-step explanation:

Given:

Half life of U-232, t1/2 = 68.8 years

Initial amount of sample of U-232, N0 = 100.0 g

Decay time, t = 344.0 years

Formula:

The radioactive decay equation is given as:

`N(t) = N(0)e^(-0.693t/t1/2)`

where N(t) = amount of the radioisotope left after time, t

N(0) = initial amount

t1/2 = half life

For U-232:

`N(t) = 100.0e^(-0.693*68.8/344.0)`

= 87.06 g

Answer 2

I think in the question you should have to find how much Uranium-232 will be left as half life of Uranium- 233 is about 1,60,000 years and will not decay much and the necessary data for that is also not provided in the question!

Uranium-232 has a half life of 68.8 years.

So, it becomes half of its current amount in 68.8years

In another 68.8 years it will become it will become 1/2 of the remaining amount .

So, in 68.8*5 or 344 years it becomes 1/2*1/2*1/2*1/2*1/2 of the present amount.

i.e. (1/2)^5 of the current amount

i.e. 1/32 of current amount.

Our sample here has 100 gm of Uranium-232,

So, it will become 100*1/32 in 344 years.

or it will become 3.125 gm

Ans) 3.125 gm

Hope it helps!!!