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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) \[\dfrac{n}{{10}}\]

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Last updated date: 16th May 2024
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Answer
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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