Question

three isotopes of silicon occur in nature: isotopes of silicon silicon - 28 silicon - 29 silicon - 30 percent abundance: 92.23 % 4.68 % 3.09 % atomic mass 27.97693 28.97649 29.97377 calculate the average atomic mass to 4 decimal places.

Explanation:

Step1: Recall the formula for average atomic mass

The formula is $\sum_{i}(m_i\times p_i)$, where $m_i$ is the atomic mass of an isotope and $p_i$ is its percent - abundance (expressed as a decimal).

Step2: Convert percent - abundances to decimals

Silicon - 28: $p_1 = 0.9223$, $m_1=27.97693$; Silicon - 29: $p_2 = 0.0468$, $m_2 = 28.97649$; Silicon - 30: $p_3=0.0309$, $m_3 = 29.97377$.

Step3: Calculate the contribution of each isotope

For Silicon - 28: $m_1\times p_1=27.97693\times0.9223 = 27.97693\times\frac{92.23}{100}=25.89302$; for Silicon - 29: $m_2\times p_2=28.97649\times0.0468 = 1.35610$; for Silicon - 30: $m_3\times p_3=29.97377\times0.0309 = 0.92619$.

Step4: Sum up the contributions

$25.89302 + 1.35610+0.92619 = 28.17531\approx28.18$

Answer:

$28.18$