The radius of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m³ of a mole of hydrogen atoms?

The correct option is 3x10⁻⁷ m³.

To find the total atomic volume of one mole of hydrogen atoms, we can break the solution down into step-by-step calculations:

Step 1: Identify the given values
The radius ($r$) of a hydrogen atom is given as 0.5 Å (Angstroms). Let's convert this value into meters (m):
$r=0.5\text{Å}=0.5\times {10}^{-10}\text{m}$

Step 2: Calculate the volume of a single hydrogen atom
Assuming a hydrogen atom is spherical, its volume ($V_{\text{atom}}$) is given by the formula for the volume of a sphere:
$V_{\text{atom}}=\frac{4}{3}\pi r^3$

Substituting the value of $r$ into the equation:
$V_{\text{atom}}=\frac{4}{3}\times 3.1416\times {\left(0.5\times {10}^{-10}\text{m}\right)}^3$
$V_{\text{atom}}=\frac{4}{3}\times 3.1416\times 0.125\times {10}^{-30}{\text{m}}^3$
$V_{\text{atom}}\approx 5.24\times {10}^{-31}{\text{m}}^3$

Step 3: Calculate the total volume of one mole of hydrogen atoms
One mole of any substance contains Avogadro's number ($N_A$) of particles:
$N_A\approx 6.022\times {10}^{23}{\text{atoms/mol}}^{}$

Multiply the volume of a single atom by the number of atoms in one mole:
$V_{\text{total}}=V_{\text{atom}}\times N_A$
$V_{\text{total}}\approx \left(5.24\times {10}^{-31}{\text{m}}^3\right)\times \left(6.022\times {10}^{23}\right)$
$V_{\text{total}}\approx 3.15\times {10}^{-7}{\text{m}}^3$

Rounding to the nearest significant figure matches the standard options:
$V_{\text{total}}\approx 3\times {10}^{-7}{\text{m}}^3$