Question

1. calculate the atomic mass of each of the following elements using your method from above. test your answer using the natures mix of isotopes and the periodic table. keep going until you can get two in a row right.

element	isotope 1		isotope 2		isotope 3		calculated average atomic mass (amu)	check answer with sim
hydrogen	1.007	99.98	2.01410	0.011	-	-
silicon	27.97	92.22	28.9764	4.685	29.97377	3.092
nitrogen	14.00	99.63	15.0001	0.364	-	-
argon	35.96	0.336	37.9627	0.063	39.96238	99.60

calculations / rough work:

Explanation:

Step1: Recall atomic - mass formula

The average atomic mass of an element with isotopes is calculated as $m=\sum_{i = 1}^{n}m_i\times p_i$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is the percentage abundance of the $i$-th isotope (expressed as a decimal).

Step2: Calculate for Hydrogen

For hydrogen, $p_1 = 0.9998$, $m_1=1.007$, $p_2 = 0.00011$, $m_2 = 2.01410$.
$m=(1.007\times0.9998)+(2.01410\times0.00011)$
$m = 1.007\times0.9998+2.01410\times0.00011=1.0068+0.000221551 = 1.007021551\approx1.007$ amu.

Step3: Calculate for Silicon

$p_1 = 0.9222$, $m_1 = 27.97$, $p_2=0.04685$, $m_2 = 28.9764$, $p_3 = 0.03092$, $m_3=29.97377$.
$m=(27.97\times0.9222)+(28.9764\times0.04685)+(29.97377\times0.03092)$
$m = 27.97\times0.9222+28.9764\times0.04685 + 29.97377\times0.03092$
$m=25.894934+1.357545+0.926799=28.179278\approx28.18$ amu.

Step4: Calculate for Nitrogen

$p_1 = 0.9963$, $m_1 = 14.00$, $p_2=0.00364$, $m_2 = 15.0001$.
$m=(14.00\times0.9963)+(15.0001\times0.00364)$
$m = 14.00\times0.9963+15.0001\times0.00364=13.9482+0.054600364 = 14.002800364\approx14.00$ amu.

Step5: Calculate for Argon

$p_1 = 0.00336$, $m_1 = 35.96$, $p_2=0.00063$, $m_2 = 37.9627$, $p_3 = 0.9960$, $m_3=39.96238$.
$m=(35.96\times0.00336)+(37.9627\times0.00063)+(39.96238\times0.9960)$
$m=0.1208256+0.023916501+39.80253048=39.947272587\approx39.95$ amu.

Answer:

Element	Calculated average atomic mass (amu)
Silicon	28.18
Nitrogen	14.00
Argon	39.95