Question

Thorium-234 has a half-life of 24.1 days. How many grams of a 150 g sample would you have after 120.5 days?

Answer 1

8.625 grams of a 150 g sample of Thorium-234 would be left after 120.5 days

Step-by-step explanation:

The nuclear half life represents the time taken for the initial amount of sample to reduce into half of its mass.

We have given that the half life of thorium-234 is 24.1 days. Then it takes 24.1 days for a Thorium-234 sample to reduced to half of its initial amount.

Initial amount of Thorium-234 available as per the question is 150 grams

So now we start with 150 grams of Thorium-234

`150 * (1)/(2)=24.1`

`75 * (1)/(2) =48.2`

`34.5 * (1)/(2) =72.3`

`17.25 * (1)/(2) =96.4`

`8.625* (1)/(2) =120.5`

So after 120.5 days the amount of sample that remains is 8.625g

In simpler way , we can use the below formula to find the sample left

`A=A_(0) \cdot (1)/(2^(n))`

Where

`A_0` is the initial sample amount

n = the number of half-lives that pass in a given period of time.