Question

average atomic mass
for each element listed below, calculate their average atomic mass. show all work.
isotope natural abundance

1. ³⁹k 93.2581%

⁴⁰k 6.7419%

1. cu - 63 69.17%

cu - 65 30.83%

1. ²⁸si 92.23%

²⁹si 4.67%
³⁰si 3.10%

1. ⁹⁰zr 51.45%

⁹¹zr 11.22%
⁹²zr 17.15%
⁹⁴zr 17.38%
⁹⁶zr 2.80%

1. ne - 20 90.93%

ne - 21 0.32%
ne - 22 8.75%

Explanation:

Step1: Recall average atomic mass formula

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

Step2: Calculate for potassium (K)

For $^{39}K$ with mass number $A_1 = 39$ and abundance $P_1=0.932581$, and $^{41}K$ with mass number $A_2 = 41$ and abundance $P_2 = 0.067419$.
$A_{avg,K}=39\times0.932581 + 41\times0.067419$
$=39\times0.932581+41\times0.067419$
$=36.370659+2.764179$
$=39.134838\approx39.13$

Step3: Calculate for copper (Cu)

For $Cu - 63$ with mass number $A_1 = 63$ and abundance $P_1 = 0.6917$, and $Cu - 65$ with mass number $A_2=65$ and abundance $P_2 = 0.3083$.
$A_{avg,Cu}=63\times0.6917+65\times0.3083$
$=43.5771+20.0395$
$=63.6166\approx63.62$

Step4: Calculate for silicon (Si)

For $^{28}Si$ with mass number $A_1 = 28$, abundance $P_1=0.9223$, $^{29}Si$ with mass number $A_2 = 29$, abundance $P_2 = 0.0467$, and $^{30}Si$ with mass number $A_3 = 30$, abundance $P_3=0.0310$.
$A_{avg,Si}=28\times0.9223+29\times0.0467 + 30\times0.0310$
$=25.8244+1.3543+0.93$
$=28.1087\approx28.11$

Step5: Calculate for zirconium (Zr)

For $^{90}Zr$ with mass number $A_1 = 90$, abundance $P_1 = 0.5145$, $^{91}Zr$ with mass number $A_2 = 91$, abundance $P_2=0.1122$, $^{92}Zr$ with mass number $A_3 = 92$, abundance $P_3 = 0.1715$, $^{94}Zr$ with mass number $A_4 = 94$, abundance $P_4=0.1738$, and $^{96}Zr$ with mass number $A_5 = 96$, abundance $P_5 = 0.0280$.
$A_{avg,Zr}=90\times0.5145+91\times0.1122+92\times0.1715+94\times0.1738+96\times0.0280$
$=46.305+10.2102+15.778+16.3372+2.688$
$=91.3184\approx91.32$

Step6: Calculate for neon (Ne)

For $Ne - 20$ with mass number $A_1 = 20$, abundance $P_1 = 0.9093$, $Ne - 21$ with mass number $A_2 = 21$, abundance $P_2=0.0032$, and $Ne - 22$ with mass number $A_3 = 22$, abundance $P_3 = 0.0875$.
$A_{avg,Ne}=20\times0.9093+21\times0.0032+22\times0.0875$
$=18.186+0.0672 + 1.925$
$=20.1782\approx20.18$

Answer:

1. $K$: $39.13$
2. $Cu$: $63.62$
3. $Si$: $28.11$
4. $Zr$: $91.32$
5. $Ne$: $20.18$