Question

98. Silicon has three naturally occurring isotopes: Si-28 with mass 27.9769 amu and a natural abundance of 92.21%, Si-29 with mass 28.9765 amu and a natural abundance of 4.69%, and Si-30 with mass 29.9737 amu and a natural abundance of 3.10%. Calculate the atomic mass of silicon.

Answer 1

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:

`\text{Average atomic mass }=\sum_(i=1)^n\text{(Atomic mass of an isotopes)}_i* \text{(Fractional abundance})_i`

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:

`\text{Average atomic mass }=[(27.9769* 0.9221)+(28.9765* 0.0469)+(29.9737* 0.0310)]`

`\text{Average atomic mass }=28.08amu`

Thus, the average atomic mass of silicon is, 28.08 amu

Answer 2

Wt Avg Atomic Wt = 28.0577 amu

Step-by-step 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