physics help please

Question

1- If the activity of a radioactive sample of Q is 28 Bq and 8.0 hours later its activity is 7.0 Bq, the half life of Q is ___h. 

 

2- Strontium-82 has a half-life of 25.0 d.  If you begin with a sample having a mass of 140 g, after ___days will you have only 17.5 g of strontium-82 left.

Answer 1

(1)

The radioactive sample Q is 28 Bq .

Let half life of radioactive is n .

8.0 hours later its activity is 7.0 Bq .

The decimal part remaining = 7/28 =1/4

Now find for half life of radioactive :

(1/2)ⁿ = decimal part remaining 

(1/2)ⁿ = 1/4

(1/2)ⁿ = (1/2)²

n = 2 half-lives .

So , the half life of Q = 8.0 hours * number of half lives 

                             = 8 * 2

                             = 16 hours  .

The half-life of a radioactive sample Q is 16 hours .

Comments

the correct answer 

Answer 2

(2)

The Strontium-82 has a half-life of 25 days .

original sample  is 140 grams .

Let n number of half lives required to decay Strontium-82 to 17.5 grams .

So  140 g * decimal part of remaining  = 17.5 

decimal part of remaining = 17.5 / 140 = 0.125 

(1/2)ⁿ = decimal part remaining 

(1/2)ⁿ = 0.125

(1/2)ⁿ = (1/2)³

n = 3 .

So , number of half lives = 3 .

17.5 g of strontium-82 left after 3 half lives is 25*3 = 75 .

Therefore after 75 days  , 17.5 g of strontium-82 left .