28.077 amu is the average mass of each isotope of silicon.
The average result of the three isotopes also gives near figure result as average atomic mass.
Explanation:
Data given:
Silicon-28 atomic mass 27.976 grams/mole, abundance is 92.23%
silicon- 29 atomic mass 28.976 grams/mole, abundance is 4.68%
silicon-30 atomic mass 29.973 grams/mole, abundance is 3.09 %
the abundance percentage is converted to decimal by dividing it with 100
so abundance is 0.9223, 0.0468, 0.0309
the occurrence of each isotope of silicon element
0.9223 x 27.976 = 25.80
0.0468 x 28.976= 1.356
0.0309 x 29.973 = 0.9261
Adding all the occurrence values of isotopes:
28.077 amu is the average atomic mass.
The average mass of all the three isotopes of silicon gives near figure.
27.976+28.976+28.976
= 28.975
from this result it can be predicted that idea involved in result obtained is correct.
The average mass of silicon present in the rock is the sum of the atomic mass of each isotope and its corresponding percentage abundance. Hence, the average mass of silicon in the rock is 28.084.
To calculate the average mass of silicon in the rock :
Sum the product of each atomic mass of silicon and the percentage abundance of each :
Silicon-28 :
Atomic mass = 27.976 g/mol
Abundance = 92.23%
Occurence = 92.23% × 27.976 = 25.802
silicon- 29 :
Atomic mass = 28.976 g/mol
Abundance = 4.68%
Occurence = 4.68% × 28.976 = 1.356
silicon-30 :
Atomic mass = 29.973 g/mol
Abundance = 3.09%
Occurence = 29.973 × 3.09% = 0.926
The sum of the occurrences of Silicon isotope :
(25.802 + 1.356 + 0.926) = 28.084
Since the actual existence of all of all 3 isotopes of Silicon equals 28.0855 amu
Then the calculated average mass of silicon is correct.
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