Question

he ${{O}^{18}}/{{O}^{16}}$ ratio in some meteorites is greater than the used to calculate the average atomic mass of oxygen one earth. The average mass of an atom of oxygen in these meteorites is ____________ that of a terrestrial oxygen atom?
(A)- equal to
(B)- greater than
(C)- less than
(D)- none of these

Answer 1

Hint: The total sum of the masses of isotopes of each of the isotopes multiplied with natural abundance is known as the Average atomic mass of the particular element. The percent of atoms found in nature is called the natural abundance. The average atomic mass can be determined as
Average atomic mass $=\dfrac{[{{M}_{A}}(Abundance{{e}_{A}})+{{M}_{B}}(Abundance{{e}_{B}})}{100}$
Where ${{M}_{A}}$ is the mass of isotope A.
${{M}_{B}}$is the mass of isotope B.
$Abundance{{e}_{A}}$is the percent abundance of A.
$Abundance{{e}_{B}}$is the percent abundance of B.

Complete step by step solution:
-According to question,
The abundance ratio of $\dfrac{{{O}^{18}}}{{{O}^{16}}}$ in some meteorites is greater than the average atomic mass of oxygen on earth.
-The higher percentage abundance of oxygen of meteorites indicates the greater average mass of oxygen present in meteorites in comparison to oxygen in the territory.
-Let us assume the percentage of ${{O}^{16}}$ being x%.
The average atomic mass of ${{O}^{16}}$on earth $=\dfrac{16\times x+(100-x)\times 18}{100}=\dfrac{16x-14x+1800}{100}=\dfrac{-2x+1800}{1000}$
The percentage of ${{O}^{18}}$ be (100-x)%.
The average atomic mass of ${{O}^{18}}$ on earth $=\dfrac{16(x-2)18(100-x+2)}{100}=\dfrac{16x-32+1800-18x+36}{100}=\dfrac{-2x+180}{100}$
-Comparing the calculated average atomic masses of ${{O}^{16}}$ and ${{O}^{18}}$:
$\dfrac{-2x+1800}{100}<\dfrac{-2x+180}{100}$
Therefore, we can say that the average atomic mass of O on meteorites will be greater.

So, the correct answer is option B.

Note: An element can have two or more different numbers of neutrons in its nucleus, but it always will have the same number of protons. The versions of an element possessing different neutrons and thus giving different masses are called isotopes. The average atomic mass for an element is calculated by adding the masses of the element’s isotopes, each multiplied by its natural abundance on earth. When doing calculations involving the atomic mass of elements or compounds, always use average atomic mass which is present on the periodic table.