Question

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 ruthenium in these samples:

isotope	mass (amu)	relative abundance
(^{101}\text{ru})	100.91	91.5%

use these measurements to complete the entry for ruthenium in the periodic table that would be used on 98765 aleks. be sure your answers have the correct number of significant digits.
caution: your correct answer will have the same format but not necessarily the same numbers as the entry for ruthenium in the periodic table we use here on earth.

Explanation:

Step1: Recall formula for average atomic mass

The formula for the average atomic mass ($A_{r}$) of an element with two isotopes is $A_{r}=m_1\times p_1 + m_2\times p_2$, where $m_1$ and $m_2$ are the masses of the isotopes and $p_1$ and $p_2$ are their relative - abundances (expressed as decimals).

Step2: Convert relative abundances to decimals

For $^{100}\text{Ru}$ with relative abundance $8.5\%$, $p_1 = 0.085$. For $^{101}\text{Ru}$ with relative abundance $91.5\%$, $p_2=0.915$. The masses are $m_1 = 99.90$ amu and $m_2 = 100.91$ amu.

Step3: Calculate average atomic mass

$A_{r}=(99.90\times0.085)+(100.91\times0.915)$
$A_{r}=8.4915 + 92.33265$
$A_{r}=100.82415\approx100.82$ (to four significant digits)

Answer:

100.82