Question

The element $X$ has the following isotopic composition:
${X^{200}} = 90\% ,{X^{199}} = 8\% ,{X^{202}} = 2\% $
The weighted average atomic mass of naturally occurring $X$ is:
A. $199u$
B. $200u$
C. $201u$
D.$202u$

Answer 1

Hint: The average atomic mass is calculated as the sum of the product of percentage amount and the atomic mass of all isotropic elements present divided by $100$. And the unit of atomic mass is AMU which is written as $u$.

Complete step by step answer:
Atomic number: It is the number of protons present in the atom of an element.
Atomic mass: It is defined as the mass (mass of nucleus present in the atom) of the atom. The unit of atomic mass is AMU which is written as $u$.
Isotopes: They are those elements which have the same atomic number but different atomic mass (i.e. they have the same number of protons but have different numbers of neutrons). For example: Carbon$ - 12$ and carbon $ - 14$ are an example of isotrope. They have the same atomic number i.e. six but they have different atomic mass i.e. for Carbon$ - 12$ atomic mass is $12$ and for carbon$ - 14$ atomic mass is $14$.
Isobars: They are those elements which have different atomic numbers but same atomic mass. For example: potassium and calcium both have atomic mass equal to $40$ but the atomic number of potassium is $19$ and the atomic number of calcium is $20$.
IsoNeutrons: They have the same number of neutrons but have different numbers of protons. For example: Boron and carbon have the same number of neutrons i.e. six but the number of protons in carbon is six but the number of protons in boron is seven.
Now according to the question we are given with the percentage amount of each isotropic element.
${X^{200}} = 90\% ,{X^{199}} = 8\% ,{X^{202}} = 2\% $
And we have to find the average atomic mass of the element. The formula to calculate the average atomic mass of an element with the given percentage amount of each isotropic element is:
Average atomic mass\[ = \dfrac{{\sum {\% {\text{amount of each isotope}} \times } {\text{Molar mass of that isotrope}}}}{{100}}\]
So the average atomic mass will be $ = \dfrac{{200 \times 90 + 199 \times 8 + 202 \times 2}}{{100}} = 199.96$ which is approximately equal to $200u$.


So, the correct answer is Option B.

Note:
The atomic number or the number of protons is represented by the symbol $Z$. Similarly the number of neutrons is represented by the symbol $N$. For a neutral atom the number of protons and the number of electrons are equal.