A sample of naturally occurring silicon consists $Si - 28$ $(27.9769 u)$ , $Si - 29$ $(28.9765 u)$ and $Si - 30$ $(29.9738 u)$ . If the atomic mass of silicon is $28.0855$ and the natural abundance of $Si - 29$ is $4.67 %$ , what are the natural abundances of $Si - 28$ and $Si - 30$ ?

Open in App

Solution

Given:
Atomic mass of $Si = 28.0855$ .
Atomic mass of $Si - 28 = 27.9769 u$
Atomic mass of $Si - 29 = 28.9765 u$
Atomic mass of $Si - 30 = 29.9738 u$
Natural abundance of $Si - 29 = 4.67 %$
Formula used:
$Atomic mass = \frac{Abundance of isotope 1}{100} \times At . mass of isotope 1 + \frac{Abundance of isotope 2}{100} \times At . mass of isotope 2 + \frac{Abundance of isotope 3}{100} \times At . mass of isotope 3$
Calculate the natural abundance of $Si - 28$ :
Let the natural abundance of $Si - 28$ be $x$ .
Then the natural abundance of $Si - 30$ will be $= 100 - 4.67 - x = 95.33 - x$
Thus,
$Atomic mass = \frac{Abundance of isotope 1}{100} \times At . mass of isotope 1 + \frac{Abundance of isotope 2}{100} \times At . mass of isotope 2 + \frac{Abundance of isotope 3}{100} \times At . mass of isotope 3 28.0855 = \frac{x}{100} \times 27.9769 + \frac{4.67}{100} \times 28.9765 + \frac{95.33 - x}{100} \times 29.9738 28.0855 = 0.279769 x + 1.3532 + 28.57 - 0.299738 x 1.8377 = 0.019969 x x = 92.03$
Therefore, natural abundance of $Si - 28$ is $92.03 %$ .
Calculate the natural abundance of $Si - 30$ :
Natural abundance of $Si - 30$ $= 95.33 - x$
Thus,
Natural abundance of $Si - 30$ $= 95.33 - 92.03$
Natural abundance of $Si - 30$ $= 3.31 %$
Therefore, natural abundance of $Si - 30$ is $3.31 %$ .

Suggest Corrections

Similar questions

The element boron occurs in nature as two isotopes having atomic masses 10u and 11u. What are the percentage abundances of these isotopes in a sample of boron having average atomic mass of 10.8u.

Q. Silicon has 92.2 % S - 28, 4.690 is Silicon 29 and the rest is Silicon 30. Calculate the average atomic mass?

Q. Chlorine has two naturally occurring isotopes,

^{35} C l

and

^{37} C l

. If the atomic mass of Cl is

35.45

, the ratio of natural abundance of

^{35} C l

and

^{37} C l

is closest to:

the avg. atomic mass of copper is 63.546u. Natural copper consists of two isotopes Cu63and Cu65. Their natural abundances are 69.09% and 30.91% respectively. If tha mass of Cu63is 62.9298u, what is the mass of Cu65??

Q. Carbon occurs in nature as a mixture of

^{12} C

and

^{13} C

. The average atomic mass of carbon is 12.011. What is the % abundance of

^{12} C

in nature?

Join BYJU'S Learning Program

A sample of naturally occurring silicon con­sists Si-28 (27.9769u), Si-29 (28.9765u) and Si-30 (29.9738u). If the atomic mass of silicon is 28.0855 and the natural abundance of Si-29 is 4.67%, what are the natural abundances of Si-28 and Si-30?

A sample of naturally occurring silicon consists $Si - 28$ $(27.9769 u)$ , $Si - 29$ $(28.9765 u)$ and $Si - 30$ $(29.9738 u)$ . If the atomic mass of silicon is $28.0855$ and the natural abundance of $Si - 29$ is $4.67 %$ , what are the natural abundances of $Si - 28$ and $Si - 30$ ?