physics

Question

The half-life of a radioactive isotope is 2.5 years.  If the activity of the original sample of this isotope was 3.2 x 10³ Bq, its activity after 5.0 years is ___x10² Bq.

 

2- A 2.0 gram sample of a radioactive isotope undergoes radioactive decay.  If the half life of the isotope is 45 minutes, the amount of the isotope that remains after 5.0 hours is ___x10^-2g 

Answer 1

(1)

The half-life of a radioactive isotope is 2.5 years .

original sample of this isotope is 3.2 x 10³ Bq .

Now find for sample after 5 years :

5 years / 2.5 years = 2 half-lives

(1/2)² = 1/4 = 0.25 (the decimal fraction remaining)

3.2 x 10³ Bq x 0.25 = 0.8 x 10³ Bq = 8 x 10² Bq .

Therefore the activity after 5.0 years is 8 x 10² Bq .

Answer 2

(2)

The half-life of a radioactive isotope is 45 minutes .

original sample of this isotope is 2 grams .

Now find for sample after 5 hours :

5 hours / 45 minutes ⇒ 5*60 / 40 = 7.5 half-lives

(1/2)^7.5 = 0.00552 (the decimal fraction remaining)

2 grams x 0.00552 = 0.01104 grams  =  1.104 x 10^-2 grams .

The amount of the isotope that remains after 5.0 hours is 1.104 x 10^-2g .

Comments

the correct answer