Question

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å : 1Å = 10-10 m. The size of a hydrogen atom is about 0.5 Å what is the total atomic volume in m3 of a mole of hydrogen atoms? 1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.​

Answer 1

Explanation:

Radius of hydrogen atom r = 0.5 = 0.5 × 10–10 mVolume of hydrogen atom = 4/3πr3 1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.Volume of 1 mole of hydrogen atoms = 6.023 × 1023 × 0.524 × 10–30 = 3.16 x 10-7 m3

Answer 2

Given :-

Radius of hydrogen atom = 0.5 A

1 mole of hydrogen contains = 6.023 × 10²³ hydrogen atoms

To Find :-

Total atomic volume in meter cube of a mole of hydrogen atoms.

Solution :-

We know that,

• r = Radius
• v = Volume

Given that,

Radius of hydrogen atom = 0.5 A = 0.5 x 10⁻¹⁰ m

By the formula,

$\underline{\boxed{\sf Volume \ of \ sphere=\dfrac{4}{3} \pi r^3}}$

Given that,

Radius (r) = 0.5 x 10⁻¹⁰ m

Substituting their values,

= (4/3) × (22/7) × (0.5 x 10⁻¹⁰)³

= 0.524 x 10⁻³⁰ m³

We know that,

1 mole of hydrogen contains = 6.023 × 10²³

Volume of 1 mole of hydrogen atom = 6.023 x 10²³ × Volume of sphere

By substituting,

= 6.023 x 10²³ × 0.524 x 10⁻³⁰

= 3.16 x 10⁻⁷ m³

Therefore, atomic volume of 1 mole of hydrogen atoms is 3.16 x 10⁻⁷ m³.