Question

The atomic masses of two elements A and B are 30 and 90 respectively. If ‘a’ g of element A contains ‘b’ atoms, then number of atoms of B in 2a g is :
(A) $\dfrac{2b}{3}$
(B) $\dfrac{b}{3}$
(C) $\dfrac{b}{4}$
(D) $\dfrac{b}{2}$

Answer 1

Hint: One mole of a substance is equal to \[6.022\text{ }\times \text{ }10{}^\text{2}{}^\text{3}\] units of that substance (such as atoms, molecules, or ions). The number \[6.022\text{ }\times \text{ }10{}^\text{2}{}^\text{3}\] is known as Avogadro's number or Avogadro's constant. Mole is equal to the ratio number of molecules to the Avogadro number.

Complete step by step answer:
Given in the question is two elements A and B with atomic masses 30 and 90 respectively. According to the question, A element of ‘a’ grams contains ‘b’ atoms, therefore, one mole of element A have ${{N}_{A}}$ number of atoms that is 30 grams of element A have ${{N}_{A}}$ atoms, (since atomic mass is 30), therefore,
$\begin{align}
 & {{N}_{A}}a=30b \\
 & b=\dfrac{{{N}_{A}}a}{30} \\
\end{align}$
Therefore, we have the relation of ‘b’ and ‘a’ for element A.

Now for B element, let us assume ‘2a’ grams of element B have x number of atoms, and 90 grams of element B have ${{N}_{A}}$ number of atoms, therefore,
\[\begin{align}
 & ({{N}_{A}})2a=90x \\
 & \left( \dfrac{({{N}_{A}})a}{30} \right)\left( \dfrac{2}{3} \right)=x \\
 & x=\dfrac{2b}{3} \\
\end{align}\]
Therefore, number of atoms in element B of ‘2a’ g is \[x=\dfrac{2b}{3}\]
So, the correct answer is “Option A”.

Note: The atomic mass of an element is the average mass of the atoms of an element measured in atomic mass unit (amu, also known as daltons, D). The atomic mass is a weighted average of all of the isotopes of that element, in which the mass of each isotope is multiplied by the abundance of that particular isotope.