Half life example questions

1.     A sample of a radioactive material contains 10¹⁸ atoms. The half life of the material is 2000 days. Calculate ;

    a)     the fraction remaining after 5000 days

    b)     the activity of the sample after 5000 days 

2.     An isotope of krypton (A=87,Z=36) has a half life of 78 minutes. Calculate the activity of 10mg of this isotope.

        DATA: The Avogadro constant N_A = 6.0  x  10²³ mol^-1

 3.     A sample of radioactive material has an activity of 9.00  x  10¹² Bq. The material has a half life of 80.0s. How long will it take for the activity to fall to 2.00  x  10¹² Bq

 4.     Potassium 44 has a half life of 20 minutes and decays to form a stable isotope Calcium 44.

    a)     write a decay equation for this transition

    b)    how many atoms would there be in 10mg of potassium 44 ?

    c)     what would be the activity of the sample ?

    d)     what would be the activity after one hour ?

    e)     what would be the ratio of potassium atoms to calcium atoms after one hour ?