Questions: A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System. Mass-spectroscopic analysis produced the following data on the isotopes of tin in these samples: isotope mass (amu) relative abundance --------- ^124 mathrmSn 123.91 92.0% ^115 mathrmSn 114.90 8.0% Use these measurements to complete the entry for tin in the Periodic Table that would be used on 98765 ALEKS. Round your entry for the atomic mass to 3 significant digits. Caution: your correct answer will have the same format but not necessarily the same numbers as the entry for tin in the Periodic Table we use here on Earth.

A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System. Mass-spectroscopic analysis produced the following data on the isotopes of tin in these samples: isotope mass (amu) relative abundance --------- ^124 mathrmSn 123.91 92.0% ^115 mathrmSn 114.90 8.0% Use these measurements to complete the entry for tin in the Periodic Table that would be used on 98765 ALEKS. Round your entry for the atomic mass to 3 significant digits. Caution: your correct answer will have the same format but not necessarily the same numbers as the entry for tin in the Periodic Table we use here on Earth.
Transcript text: A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System. Mass-spectroscopic analysis produced the following data on the isotopes of tin in these samples: \begin{tabular}{|c|c|c|} \hline isotope & \begin{tabular}{c} mass \\ $(\mathrm{amu})$ \end{tabular} & \begin{tabular}{c} relative \\ abundance \end{tabular} \\ \hline${ }^{124} \mathrm{Sn}$ & 123.91 & $92.0 \%$ \\ \hline${ }^{115} \mathrm{Sn}$ & 114.90 & $8.0 \%$ \\ \hline \end{tabular} Use these measurements to complete the entry for tin in the Periodic Table that would be used on 98765 ALEKS. Round your entry for the atomic mass to 3 significant digits. Caution: your correct answer will have the same format but not necessarily the same numbers as the entry for tin in the Periodic Table we use here on Earth. $\square$
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Solution

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Solution Steps

Step 1: Identify the Given Data

We are given the following data for the isotopes of tin:

  • Isotope \( {}^{124}\mathrm{Sn} \) with a mass of 123.91 amu and a relative abundance of 92.0%
  • Isotope \( {}^{115}\mathrm{Sn} \) with a mass of 114.90 amu and a relative abundance of 8.0%
Step 2: Convert Relative Abundance to Decimal Form

Convert the relative abundances from percentages to decimal form:

  • For \( {}^{124}\mathrm{Sn} \): \( 92.0\% = 0.920 \)
  • For \( {}^{115}\mathrm{Sn} \): \( 8.0\% = 0.080 \)
Step 3: Calculate the Weighted Average Atomic Mass

The atomic mass of tin on 98765 ALEKS is calculated using the weighted average formula: \[ \text{Atomic Mass} = (123.91 \times 0.920) + (114.90 \times 0.080) \]

Step 4: Perform the Calculations

Calculate each term separately: \[ 123.91 \times 0.920 = 114.0002 \] \[ 114.90 \times 0.080 = 9.1920 \]

Add these results together to find the weighted average atomic mass: \[ \text{Atomic Mass} = 114.0002 + 9.1920 = 123.1922 \]

Step 5: Round to 3 Significant Digits

Round the atomic mass to 3 significant digits: \[ \text{Atomic Mass} \approx 123 \]

Final Answer

\[ \boxed{123} \]

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