Question

Out of 500 silicon atoms: 460 are si-28, which has a mass of 27.98 amu 25 are si-29, which has a mass of 28.98 amu and 15 are si-30, which has a mass of 29.97 amu. what is the average atomic mass of silicon? (round to 2 decimal places) (hint: they did not give you percentages, but you can calculate the percentages and then do the problem)

Answer 1

Average mass can be calculated by taking average of mass of each isotopes considering their abundance.

First calculate the percentage of each isotope.

Si(28) is 460 out of 500, percentage will be \frac{460}{500}\times 100=92%

Si-29 is 25 out of 500, percentage will be \frac{25}{500}\times 100=5%

Si-30 is 15 out of 500, percentage will be \frac{15}{500}\times 100=3%

Formula for average mass used will be:

Average mass=(% of Si-28×mass of Si-28)+(% of Si-29×mass of Si-29)+(% of Si-30×mass of Si-30)

=(0.92×27.98) amu+(0.05×28.98) amu+(0.03×29.97) amu

=(25.74+1.45+0.899) amu

=28.09 amu

Thus, average atomic mass of silicon is 28.09 amu.

Answer 2

Answer;

=28.09 amu

Explanation;

In this problem, they did not give us the percentages. However, since we know the number of atoms, we can easily calculate the percentages. For example:  

(460 X 100)/500 = 92%  

If we do this for all three isotopes,

(460 × 25)/500 = 5 %

(460 × 15) /500 = 3%

-We get 92%, 5%, and 3%. (We'll assume these are absolute numbers for determining our significant figures).

Now the problem is just like the previous one. First convert the percentages into decimals. Then multiply those decimals by the masses and add. Here's the solution:  

= (0.92) X (27.98 amu) + (0.05) X (28.98 amu) + (0.03) X (29.97 amu)

= 25.74 amu  +  1.449 amu  + 0.8991 amu

= 28.09 amu