Question

A mystery element occurs in nature as three isotopes. Isotope A has a mass of 15.994915 amu and its abundance is 99.762%; Isotope B has a mass of 16.999132 amu and its abundance is 0.0380%; Isotope C has a mass of 17.999160 amu and its abundance is 0.2000%. From this data, calculate the atomic mass of the element.

Answer 1

The atomic mass of the mystery element with three naturally occurring isotopes is calculated by finding the weighted average of the isotopic masses, taking into account their respective abundances. The atomic mass is found to be 16.035 amu when rounded to five significant figures.

Step-by-step explanation:

The atomic mass of an element can be calculated using the weighted average of the masses of its naturally occurring isotopes. To calculate this, we need to consider the mass of each isotope and its abundance in nature. Using the given data for the mystery element with isotopes A, B, and C, we apply the following steps:

1. Convert the percent abundance of each isotope to a decimal by dividing by 100.
2. Multiply the mass of each isotope by its corresponding decimal abundance.
3. Add the results from step 2 to find the weighted average atomic mass of the element.

For isotope A:

(0.99762 × 15.994915 amu) = 15.992081863 amu

For isotope B:

(0.000380 × 16.999132 amu) = 0.0064595504 amu

For isotope C:

(0.002000 × 17.999160 amu) = 0.03599832 amu

Add the contribution from each isotope to get the atomic mass of the element:

15.992081863 amu + 0.0064595504 amu + 0.03599832 amu = 16.0345397334 amu

Rounded to five significant figures, the atomic mass is 16.035 amu.