Calculating average atomic mass

[Akshath]

The relative abundance of various isotopes of silicon is as Si(28) = 92.25%, Si(29) = 4.65% and Si(30) = 3.10 % . Calculate the average atomic mass of Silicon.

Ans : 28.11 u

Attempt. : I don't know how to start this problem .

 

[ycheff]

0.9225*28 + 0.0465*29 + 0.0310*30 = 28.1085

 

[Akshath]

Thanx. This holds good for all elements ( to calculate average atomic mass of Isotopes) ?

 

[Borek]

Yes, average atomic mass is always a weighted average.

 

[LudusRex]

To calculate the average atomic mass of an element, we need to take into account the relative abundance of each isotope and its corresponding atomic mass. In this case, we have three isotopes of silicon with their relative abundances given as percentages.

The first step is to convert these percentages into decimal form by dividing each percentage by 100. This will give us the proportion of each isotope in the overall sample.

Si(28) = 92.25% / 100 = 0.9225
Si(29) = 4.65% / 100 = 0.0465
Si(30) = 3.10% / 100 = 0.0310

Next, we multiply the proportion of each isotope by its atomic mass.

Si(28) = 0.9225 x 28 = 25.83
Si(29) = 0.0465 x 29 = 1.35
Si(30) = 0.0310 x 30 = 0.93

Then, we add these values together to get the average atomic mass of silicon.

Average atomic mass of silicon = 25.83 + 1.35 + 0.93 = 28.11 u

Therefore, the average atomic mass of silicon is 28.11 u. This is the weighted average of all the isotopes of silicon taking into account their relative abundances.