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Physics · UNITS AND MEASUREMENT

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The size of a hydrogen atom is about \( 0.5 \text{ \AA} \). The total atomic volume of 1 mole of hydrogen atoms in \( \text{m}^3 \) is closest to: (Take \( \pi = 3.14 \), Avogadro's number \( N_A = 6.02 \times 10^{23}\text{ mol}^{-1} \))

  1. A
    \( 3.15 \times 10^{-7}\text{ m}^3 \)
  2. B
    \( 5.24 \times 10^{-31}\text{ m}^3 \)
  3. C
    \( 6.02 \times 10^{-23}\text{ m}^3 \)
  4. D
    \( 1.31 \times 10^{-31}\text{ m}^3 \)
View Answer & Solution

Correct answer · Option A

\( 3.15 \times 10^{-7}\text{ m}^3 \)

Explanation

Volume of 1 atom \( V_1 = \frac{4}{3}\pi r^3 = \frac{4}{3} (3.14) (0.5 \times 10^{-10})^3 \approx 5.23 \times 10^{-31}\text{ m}^3 \). Total volume for 1 mole \( = V_1 \times N_A \approx 3.15 \times 10^{-7}\text{ m}^3 \).
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