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# If x g of A(atomic mass 50) has n atoms, how many atoms are there in 20g of B(atomic weight100)(A) N(B) 10n(C) 20n(D) $\dfrac{n}{{10}}$

Last updated date: 16th May 2024
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Hint The number of atoms in a given substance is proportional to the no. of moles of that substance. We thus need to find the number of moles of B compared to the number of moles of A.

Complete step by step solution The number of atoms in 1 mole of a substance is equal to the Avogadro's number which is $6.022 \times {10^{23}}$. The number of moles of any substance is given by:
$m\, = \,\dfrac{{given{\text{ }}mass}}{{molar{\text{ }}mass/atomic{\text{ }}mass}}$
Therefore the number of atoms of A is given by
$n\, = \,{N_a}\dfrac{{given{\text{ }}mass}}{{molar{\text{ }}mass/atomic{\text{ }}mass}}$
Where N is the Avogadro number
For atom A, we have
${n_a}\, = \,{N_a}\dfrac{x}{{50}} \\ {n_b}\, = \,{N_a}\dfrac{{20x}}{{100}} \\$
Dividing the 2 equations, we get:
$\dfrac{{{n_b}}}{{{n_a}}}\, = \,\dfrac{{50(20x)}}{{100x}}$
${n_b} = \,10{n_a}$

Therefore the option with the correct answer is option B

Note n this question, the atomic weight of element B is given instead of mass. This is just a misnomer because atomic weight and atomic mass are effectively the same things only