Question

The astronaut then measures the abundance of silicon on the new planet, obtaining the following results: isotope abundance (%) mass (amu) 28si 73.71 27.98 29si 14.93 28.98 30si 11.36 29.97 what is the atomic mass of silicon for this planet?

Answer 1

To compute for the average atomic mass of silicon, we need to have the atomic masses of each of the isotopes and their relative percent abundance. We then get the summation of the product of the atomic mass and percentage. 

atomic mass = (.7371) 27.98 + (0.1493) 28.98 + (0.1136) 29.97 = 28.36 amu

Answer 2

Answer: The average atomic mass of the silicon will be 28.36 u.

Explanation:

Average atomic mass of an element is defined as the sum of masses of the isotopes each multiplied by its natural fractional abundance.

Formula that is used to calculate the average atomic mass follows:

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

We are given:

• For $^{28}\textrm{Si}$

Mass of isotope $^{28}\textrm{Si}=27.98u$

Percentage abundance of $^{28}\textrm{Si}=73.71\%$

Fractional abundance of $^{28}\textrm{Si}=0.7371$

• For $^{29}\textrm{Si}$

Mass of isotope $^{29}\textrm{Si}=28.98u$

Percentage abundance of $^{28}\textrm{Si}=14.93\%$

Fractional abundance of $^{28}\textrm{Si}=0.1493$

• For $^{30}\textrm{Si}$

Mass of isotope $^{30}\textrm{Si}=29.97u$

Percentage abundance of $^{30}\textrm{Si}=11.36\%$

Fractional abundance of $^{30}\textrm{Si}=0.1136$

Putting values in equation 1, we get:

$\text{Average atomic mass of Silicon}=[(27.98\times 0.7371)+(28.98\times 0.1493)+(29.97\times 0.1136)]$

$\text{Average atomic mass of Silicon}=28.36u$

Hence, the average atomic mass of silicon will be 28.36 u.