Question

The element X has the following isotopic composition:
${X^{200}} = 90\% ,{X^{199}} = 8.0\% ,{X^{202}} = 2.0\%$
The weighted average atomic mass of the naturally occurring X is
A.199 u
B.200 u
C.201 u
D.202 u

Answer 1

Isotopic composition is a powerful tool in petroleum forensic and has found many and varied applications in fact fields. It has proven most useful as a component in assignments based upon multiple lines of evidence. Isotopic composition is imparted to oil during its formation. The average atomic mass of an element is the sum of the mass of its isotopes.

Complete step by step answer:
Here we find the average atomic mass naturally by the isotopic composition of the element.
We have some values of isotopic mass and percentage of occurrence.
The value of average atomic mass finds by the following equation:
Average atomic mass $= \dfrac{{{A_1}{X_1} + {A_2}{X_2} + {A_3}{X_3}}}{{3 \times 100}}$
Here, A= Isotopic mass
X=Percentage of occurrence
Average atomic mass $= \dfrac{{200 \times 90 + 199 \times 8 + 202 \times 2}}{{3 \times 100}}$
$= 199.96 \\\ \cong 200u \\\$

Hence option B is correct.

Additional information:
Isotopes of an element have the same number of protons and electrons, but the different number of neutrons. The average mass of isotope is the same of the relative atomic mass of the element. Different isotope of an element has the same number of an atomic number, but different mass numbers. That is because each isotope of an element contains a different number of neutrons.

Note:
Isotopes are sometimes shown by the name of the element, followed by the mass number. As a percentage, find the average atomic mass and set up the relative abundance problems. Then find the value of average atomic mass.