# Question #09099

Sep 14, 2015

Element $\text{X}$ is silicon.

#### Explanation:

The idea here is that you need to use the atomic masses of the isotopes and their respective abundances to find the average atomic mass of element $\text{X}$.

Even without doing any calculations, you can guess that the average atomic mass of elemnt $\text{X}$ will be very close to 28.00 amu due to the very high abundance of the $\text{^28"X}$ isotope.

Its high abundance tells you that it contributes most to the average atomic mass, so you can expect the atomic mass of element $\text{X}$ to be close to that value.

You can use fractional abundances to calculate the contribution each isotope has to the average atomic mass

$\text{For " ""^28"X":" " 92.23/100 * "27.977 amu" = "25.80319 amu}$

$\text{For " ""^29"X":" "4.67/100 * "28.976 amu" = "1.35318 amu}$

$\text{For " ""^30"X":" "3.10/100 * "29.974 amu" = "0.92919 amu}$

The average atomic mass of the element will be the sum of each isotope's contribution

$\text{avg. atomic mass" = sum"isotope contribution}$

This means that you have

$25.80319 + 1.35318 + 0.92919 = \textcolor{g r e e n}{\text{28.08556 amu}}$

A quick look in the periodic table will reveal that element $\text{X}$ is silicon.