Question

"A sample of silicon has an average atomic mass of 28.084amu. In the sample, there are three isotopic forms of silicon. About 92.22% of silicon atoms are 27.9769amu, which have the mass of 28Si; about 4.68% are 28.9764amu, which have the mass of 29Si, and the remaining isotope, 30Si, has a mass of 29.9737amu. Calculate the percent isotopic composition of 30Si."

Answer 1

Answer: The percentage abundance for $_{14}^{30}\textrm{Si}$ isotope is 3.09 %.

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:

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

We are given:

Let the fractional abundance for $_{14}^{28}\textrm{Si}$ isotope be 'x'

• For $_{14}^{28}\textrm{Si}$ isotope:

Mass of $_{14}^{28}\textrm{Si}$ isotope = 27.9769 amu

Percentage abundance of $_{14}^{28}\textrm{Si}$ isotope = 92.22 %

Fractional abundance of $_{14}^{28}\textrm{Si}$ isotope = 0.9222

• For $_{14}^{29}\textrm{Si}$ isotope:

Mass of $_{14}^{28}\textrm{Si}$ isotope = 28.9764 amu

Percentage abundance of $_{14}^{28}\textrm{Si}$ isotope = 4.68%

Fractional abundance of $_{14}^{28}\textrm{Si}$ isotope = 0.0468

• For $_{14}^{30}\textrm{Si}$ isotope:

Mass of $_{14}^{30}\textrm{Si}$ isotope = 29.9737 amu

Fractional abundance of $_{14}^{30}\textrm{Si}$ isotope = x

• Average atomic mass of silicon = 28.084 amu

Putting values in equation 1, we get:

$28.084=[(27.9769\times 0.9222)+(28.9764\times 0.0468)+(29.9737\times x)]\\\\x=0.0309$

Converting this fractional abundance into percentage abundance by multiplying it by 100, we get:

$\Rightarrow 0.0309\times 100=3.09\%$

Hence, the percentage abundance for $_{14}^{30}\textrm{Si}$ isotope is 3.09 %.