Among 10⁻⁹ g (each) of the following elements, which one will have the highest number of atoms?
Element: Pb, Po, Pr and Pt

Solution

Chemistry ma’am · 2 steps

Same mass for all four, so the lightest atom gives the most atoms. Find the smallest molar mass.

1. Count the atoms. Number of atoms = moles × N_A, and moles = mass divided by molar mass M. The mass is fixed at 10⁻⁹ g, so the element with the smallest M gives the most atoms.

   N = m/M × N_A ⇒ N ∝ 1/M

   Element	Atomic number	Molar mass (g mol⁻¹)	Atoms in 10⁻⁹ g
   Pr (praseodymium)	59	140.9	4.27 × 10¹²
   Pt (platinum)	78	195.1	3.09 × 10¹²
   Pb (lead)	82	207.2	2.91 × 10¹²
   Po (polonium)	84	209	2.88 × 10¹²

2. So. Pr has the smallest molar mass of the four, so 10⁻⁹ g of Pr holds the most atoms. The answer is (a).

The idea to keep. For equal masses, the number of atoms goes as 1/M. The lightest element always wins. Here a lower atomic number in the periodic table points you to it quickly.

Answer from the NTA final answer key. Solution by PrepWiser.