Lead - 210

The half-life of Pb 210 is 20 years. Find the initial number of disintegrations per second for 1.0g of this isotope of lead.

210g lead contains N_A(6.02 x 10²³) atoms

therefore 1 g lead contains 6.02 x 10²³/210 atoms

(LEAVE IT IN THIS FORM… IT IS NOT A GOOD IDEA TO KEEP ON WORKING OUT SUBSTAGES)

N₀ = 6.02 x 10²³/210

dN/dt = ?

half life

= 20 years

= 20 x 365.25 days

= 20 x 365.25 x 24 hours

= 20 x 365.25 x 24 x 60 hours

= 20 x 365.25 x 24 x 60 x 60 seconds

= 6.31 x 10⁸ seconds

l = - ln2/half life = - 0.693/(6.31 x 10⁸)

= - (- 0.693 /(6.31 x 10⁸)) x (6.02 x 10²³/210)

= (0.693 x 6.02 x 10^{23 )}/ (210 x 6.31 x 10⁸)

= 3.1 x 10¹² s^-1