Question

Silicon has three naturally occurring isotopes. Silicon-28 has a mass of 27.98 and a relative abundance of 92.23%. Silicon-29 has a mass of 28.98 and a relative abundance of 4.68%. Silicon-30 has a mass of 29.97 and a relative abundance of 3.09%. What is the weighted average atomic mass of silicon?

Answer 1

The weighted average atomic mass of Silicon is 28.1

(27.98 x .9223) + (28.98 x .0468) + (29.97 x .0309) 
= 25.81 + 1.36 + .93
= 28.1

Answer 2

Answer : The atomic mass of the silicon is, 28.09 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:

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

As we are given that,

Mass of isotope, Silicon-28 = 27.98 amu

Percentage abundance of isotope, Silicon-28 = 92.23 %

Fractional abundance of isotope, Silicon-28 = 0.9223

Mass of isotope, Silicon-29 = 28.98 amu

Percentage abundance of isotope, Silicon-29 = 4.68 %

Fractional abundance of isotope, Silicon-29 = 0.0468

Mass of isotope, Silicon-30 = 29.97 amu

Percentage abundance of isotope, Silicon-30 = 3.09 %

Fractional abundance of isotope, Silicon-30 = 0.0309

Now put all the given values in above formula, we get:

$\text{Average atomic mass of element}=\sum[(27.98\times 0.9223)+(28.98\times 0.0468)+(29.97\times 0.0309)]$

$\text{Average atomic mass of element}=28.09amu$

Therefore, the atomic mass of the silicon is, 28.09 amu