Question

An element ‘X’ has the following isotopic composition;
\[{}^{200}X:90%\]
\[{}^{199}X:8.0%\]
\[{}^{202}X:2.0%\]
The weighted average atomic mass of the naturally occurring element ‘X’ is closest to:
(A) 199amu
(B) 200amu
(C) 201amu
(D) 202amu

Answer 1

Hint: Brush up the nuclear chemistry concepts. In the question, atomic masses and percentage composition of each isotope is given. We know that average atomic mass is the summation of the product of the atomic mass of each isotope and its abundance divided by 100. Just substitute the values to get the answer.

Complete step by step solution:
-Let’s take a look at the data given in the question.
-We have been given atomic masses of three isotopes of an element and its composition in percentage which indicates the abundance.
\[{}^{200}X:90%\]
\[{}^{199}X:8.0%\]
\[{}^{202}X:2.0%\]
-We need to find the average atomic mass of the natural isotope of element ‘X’.
-Formula for finding weight average atomic mass is the summation of the product of the atomic mass of each isotope and its abundance divided by 100. That is, the average atomic mass is $\dfrac{\sum{(atomic\,mass\times abundance)}}{100}$.
-Therefore, substituting the values we get, $\dfrac{\left( 200\times 90 \right)+\left( 199\times 8 \right)+\left( 202\times 2 \right)}{100}=199.96amu$
-Therefore, the average atomic mass of the natural isotope of element ‘X’ is 199.6amu which is approximately equal to 200amu.

Therefore, the answer is option (B).

Note: Remember the formula for calculation of average atomic weight. A short-cut to answer this question will be to find out which of the given isotopes is the most abundant. Here isotope having atomic mass 200amu is most abundant, so weight average atomic mass will be that value only because other isotopes are present in very less quantity and we are calculating the average of their atomic masses. More abundant the isotope, the more stable it is and naturally it will occur in that form only.