Given:
1 angstrom (Å) = 1 × 10−10 m
Size (diameter) of a hydrogen atom = 0.5 Å
Hence, radius of a hydrogen atom:
r = 0.25 Å = 0.25 × 10−10 m
Number of atoms in one mole:
NA = 6.02 × 1023
Step 1: Volume of one hydrogen atom
Assuming a hydrogen atom to be spherical, its volume is:
V1 = (4/3)πr3
V1 = (4/3)π (0.25 × 10−10)3
V1 = (4/3)π × 0.015625 × 10−30
V1 ≈ 6.5 × 10−32 m3
Step 2: Total atomic volume of one mole of hydrogen atoms
Vtotal = NA × V1
Vtotal = (6.02 × 1023) × (6.5 × 10−32)
Vtotal ≈ 3.9 × 10−8 m3
Final Answer:
The total atomic volume of one mole of hydrogen atoms is:
≈ 4 × 10−8 m3