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Physics · UNITS AND MEASUREMENT

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One mole of an ideal gas at STP occupies \( 22.4\text{ L} \). Taking the size of a hydrogen molecule to be about \( 1\text{ \AA} \), what is the ratio of molar volume to the atomic volume of a mole of hydrogen molecules?

  1. A
    \( \approx 3.2 \times 10^3 \)
  2. B
    \( \approx 6.4 \times 10^4 \)
  3. C
    \( \approx 2.2 \times 10^5 \)
  4. D
    \( \approx 1.1 \times 10^4 \)
View Answer & Solution

Correct answer · Option B

\( \approx 6.4 \times 10^4 \)

Explanation

Molar volume \( = 22.4\text{ L} = 22.4 \times 10^{-3}\text{ m}^3 \). Atomic volume of one mole \( = N_A \times \frac{4}{3}\pi r^3 \). Taking \( r = 0.5 \times 10^{-10}\text{ m} \), ratio comes out to be of the order of \( 6.4 \times 10^4 \).
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