Questions: Use the mass spectrum of lead to estimate the atomic mass of lead. Estimate the mass and percent intensity values from the graph to three significant figures. The peak representing Pb-204 has a percent intensity of 2.70%; the peak representing Pb-206 has a percent intensity of 46.0%; the peak representing Pb-207 has a percent intensity of 23.1%; and the peak representing Pb-208 has a percent intensity of 22.6%. Express your answer to three significant figures and include the appropriate units.

Use the mass spectrum of lead to estimate the atomic mass of lead.

Estimate the mass and percent intensity values from the graph to three significant figures. The peak representing Pb-204 has a percent intensity of 2.70%; the peak representing Pb-206 has a percent intensity of 46.0%; the peak representing Pb-207 has a percent intensity of 23.1%; and the peak representing Pb-208 has a percent intensity of 22.6%. Express your answer to three significant figures and include the appropriate units.

Transcript text: Use the mass spectrum of lead to estimate the atomic mass of lead. Estimate the mass and percent intensity values from the graph to three significant figures. The peak representing $\mathrm{Pb}-204$ has a percent intensity of $2.70 \%$; the peak representing $\mathrm{Pb}-206$ has a percent intensity of $46.0 \%$; the peak representing $\mathrm{Pb}-207$ has a percent intensity of $23.1 \%$; and the peak representing $\mathrm{Pb}-208$ has a percent intensity of $22.6 \%$. Express your answer to three significant figures and include the appropriate units.

Solution

Solution Steps

Step 1: Identify the Masses and Percent Intensities

From the mass spectrum graph, identify the masses and their corresponding percent intensities:

Mass 204: 1.4%
Mass 206: 24.1%
Mass 207: 22.1%
Mass 208: 52.4%

Step 2: Convert Percent Intensities to Decimal Form

Convert the percent intensities to decimal form by dividing each by 100:

Mass 204: 0.014
Mass 206: 0.241
Mass 207: 0.221
Mass 208: 0.524

Step 3: Calculate the Weighted Average Atomic Mass

Multiply each mass by its corresponding decimal intensity and sum the results to find the weighted average atomic mass: \[ \text{Atomic Mass} = (204 \times 0.014) + (206 \times 0.241) + (207 \times 0.221) + (208 \times 0.524) \] \[ \text{Atomic Mass} = 2.856 + 49.646 + 45.747 + 108.992 \] \[ \text{Atomic Mass} = 207.241 \]