Question

My alpha radiation source is polonium-210. When new, the activity of the source is 0.1 microcurie.

1.What is the half-life?

2.Calculate the decay constant.

3.What is the activity of the new source in bequerels?

4.How many ²¹⁰Po atoms are present in the source when it

Answer 1

1. Polonium 210 has a half life of 138 days.

2. The half life and decay constant the related by the formula as follows:

k = 0.693/t_1/2 here k = decay constant, t_1/2 is half life. therefore,

k = 0.693/138 = 0.00502/day

3. 1 curie = 3.7 x 10⁷ Bq

therefore, 0.1 microcurie is 3700 Bq.

4. 210 grams of Polonium contains 6.023 x 10²³ atoms therefore,

1gram will contain 6.023 X 10²³ / 210 = 0.0286 X 10²³ atoms.

5. To calculate the activity after 2 years convert 2 years into days 365 x 2 = 730 days

use the A = A_oe^-kt here A is activity after time t, Ao is initial activity, k is decay constant, t is the time, therefore

A = 0.1 e ^{- 0.00502(730)} = 0.00256 microcurie

6. Again use above equation

A= Ao/10 , Ao = 0.1

In 10 = kt

t = 2.302/0.00502 = 458 days = 1.25 years

7. 206 g of leads has 6.02 x 10²³ atoms

1 g = 6.02 x 1023 / 206 = 0.029 X 10²³

No= 0.029 x 10²³ if we know the half life of Pb 206 then we can calculate the no. of atoms present after 6 months by using the this equation N = No e ^{- kt}