Question

You just discovered a radioactive element with an atomic mass of 250 g/mol. A sample of 9.61 ng of it decays at a rate of 8 atoms per second. What is its half-life, in years? Use 6.022 × 1023 for Avogadro's number and 365.25 for the number of days in a year.

A substance that undergoes zero-order kinetics has an initial concentration of 0.500 M. After 5.00 s, its concentration is 0.292 M. What will be the concentration after 8.00 s?

Answer 1

Ans 1

9.61 ng = 9.61 x 10^-9 grams = (9.61 x 10^-9) / 250 = 3.844 x 10^-11 moles

1 mole has 6.022 x 10²³ atoms

So 3.844 x 10^-11 moles will have 3.844 x 10^-11 x 6.022 x 10²³ = 2.31 x 10¹³ atoms

The half life period is the time in which the sample reduces to half of its value.

So the decayed amount will be (2.31 x 10¹³) / 2 = 1.16 x 10¹³ atoms

Since 8 atoms are decayed per second , so the time required for this decay will be :

(1.16 x 10¹³) / 8 = 1.45 x 10¹² seconds

Number of years = (1.45 x 10¹²) / ( 60 x 60 x 24 x 365.25)

= 45845.87 years