Question

3.) lead has four naturally occurring isotopes: isotopes of lead: percent abundance: atomic mass: a. lead-204 relative abundance of 1.4% mass of 204 amu b. lead-206 relative abundance of 24.1% mass of 206 amu c. lead-207 relative abundance of 22.1% mass of 207 amu d. lead-208 relative abundance of 52.4% mass of 208 amu calculate the average atomic mass for the four isotopes of lead.

Explanation:

Step1: Convert percentages to decimals

For Lead - 204: \(1.4\% = 0.014\)
For Lead - 206: \(24.1\%=0.241\)
For Lead - 207: \(22.1\% = 0.221\)
For Lead - 208: \(52.4\%=0.524\)

Step2: Multiply each isotope's mass by its decimal abundance

Lead - 204: \(204\times0.014 = 2.856\)
Lead - 206: \(206\times0.241=206\times0.2 + 206\times0.04+206\times0.001=41.2+8.24 + 0.206 = 49.646\)
Lead - 207: \(207\times0.221 = 207\times0.2+207\times0.02 + 207\times0.001=41.4+4.14+0.207 = 45.747\)
Lead - 208: \(208\times0.524=208\times0.5+208\times0.02+208\times0.004 = 104+4.16+0.832=108.992\)

Step3: Sum the products

\(2.856 + 49.646+45.747 + 108.992=(2.856+49.646)+(45.747 + 108.992)=52.502+154.739 = 207.241\)

Answer:

The average atomic mass of lead is approximately \(207.24\) amu (rounded to two decimal places)