Question

The three major isotopes of lead are Pb-206, Pb-207 and Pb-208. If they exist in the abundances 19.4%, 40.3% and 40.3% respectively, what is the AVERAGE ATOMIC MASS of lead? *SHOW YOUR WORK!

Answer 1

The average atomic mass of lead is the average of the masses of its isotopes $A_i$ , weighted by their abundance $f_i$ :

$A = \sum_if_iA_i$ .

The masses of isotopes Pb-206, Pb-207 and Pb-208 are 206 amu, 207 amu and 208 amu, respectively. Their abundances $f_i$ must be expressed as fractions (divide the abundance expressed in percentage by 100 and you get it expressed in fraction) and therefore are 0.194, 0.403 and 0.403 for Pb-206, Pb-207 and Pb-208, respectively:

$A = 0.194·206+0.403·207+0.403·208$

$A = 207.209$ amu.

Answer: the average atomic mass of lead is 207.209 amu.

Note: actually, the exact natural abundances of the stable isotopes of lead are 1.4%, 24.1%, 22.1% and 52.4% for Pb-204, Pb-206, Pb-207 and Pb-208, respectively.