Answer:
Wt Avg Atomic Wt = 28.0577 amu
Explanation:
Atomic Mass = ∑Wt Avg contributions of isotopes of an element
Si-28 => 92.21% => 0.9221 decimal fraction => Wt Avg Si-28 = 0.9221(27.9769) = 25.7695 amu
Si-29 => 4.69% => 0.0469 decimal fraction => Wt Avg Si-29 = 0.0469(28.9765) = 1.3590 amu
Si-30 => 3.10% => 0.0310 decimal fraction => Wt Avg Si-30 = 0.0310(29.9737) = 0.9292
Wt Avg Atomic Wt = ∑Wt Avg Contributions = (25.7695 + 1.3590 + 0.9292)amu = 28.0577 amu
Answer : The average atomic mass of silicon is, 28.08 amu
Explanation :
Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.
Formula used to calculate average atomic mass follows:
[tex]\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i[/tex]
For isotope Si-28 :
Mass of isotope Si-28 = 27.9769 amu
Fractional abundance of isotope Si-28 = 92.21 % = 0.9221
For isotope Si-29 :
Mass of isotope Si-29 = 28.9765 amu
Fractional abundance of isotope Si-29 = 4.69 % = 0.0469
For isotope Si-30 :
Mass of isotope Si-30 = 29.9737 amu
Fractional abundance of isotope Si-30 = 3.10 % = 0.0310
Putting values in equation 1, we get:
[tex]\text{Average atomic mass }=[(27.9769\times 0.9221)+(28.9765\times 0.0469)+(29.9737\times 0.0310)][/tex]
[tex]\text{Average atomic mass }=28.08amu[/tex]
Thus, the average atomic mass of silicon is, 28.08 amu
