Question

the radius of a muonic hydrogen atom is 2.5*10^-13m.what is the total atomic volume in m^3 of a mole of such hydrogen atom

Answer 1

Answer ⇒ The volume of 1 mole of hydrogen atoms is 7.89 × 10⁻¹⁴ m³.

Explanation ⇒ Radius of the Atom = 2.5 × 10⁻¹³

We know that the shape of atom is spherical.

Thus, Volume of atom = Volume of sphere

= 4/3 πr³

= 4/3 × 22/7 × 2.5³ × 10⁻³⁹

= 65.476 × 10⁻³⁹

Now, One mole of Hydrogen consist of 12.044 × 10²³ atoms.

∴ Volume of one mole of atoms of hydrogen = 12.044 × 10²³ × Volume of 1 atom of Hydrogen.

= 12.044 × 10²³ × 65.476 × 10⁻³⁹

= 788.6 × 10⁻¹⁶

= 7.89 × 10⁻¹⁴ m³

Hence, the volume of 1 mole of hydrogen atoms is 7.89 × 10⁻¹⁴ m³.

Hope it helps.