2. calculate the atomic mass of each of the following elements using your method from above. test your…

2. 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.\n| element | isotope 1 | | isotope 2 | | isotope 3 | | calculated average atomic mass (amu) | check answer with sim | |\n| ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| | mass (amu) | %age | mass (amu) | %age | mass (amu) | %age | | yes | no |\n| hydrogen | 1.007 | 99.98 | 2.01410 | 0.011 | - | - | | | |\n| silicon | 27.97 | 92.22 | 28.9764 | 4.685 | 29.97377 | 3.092 | | | |\n| nitrogen | 14.00 | 99.63 | 15.0001 | 0.364 | - | - | | | |\n| argon | 35.96 | 0.336 | 37.9627 | 0.063 | 39.96238 | 99.60 | | | |\ncalculations / rough work:

2. 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.\n| element | isotope 1 | | isotope 2 | | isotope 3 | | calculated average atomic mass (amu) | check answer with sim | |\n| ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| | mass (amu) | %age | mass (amu) | %age | mass (amu) | %age | | yes | no |\n| hydrogen | 1.007 | 99.98 | 2.01410 | 0.011 | - | - | | | |\n| silicon | 27.97 | 92.22 | 28.9764 | 4.685 | 29.97377 | 3.092 | | | |\n| nitrogen | 14.00 | 99.63 | 15.0001 | 0.364 | - | - | | | |\n| argon | 35.96 | 0.336 | 37.9627 | 0.063 | 39.96238 | 99.60 | | | |\ncalculations / rough work:

Answer

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)
Hydrogen 1.007
Silicon 28.18
Nitrogen 14.00
Argon 39.95