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Physics · UNITS AND MEASUREMENT

हिन्दी

The unit of length convenient on the atomic scale is known as an angstrom (\( \text{\AA} \)). Given that \( 1\text{ \AA} = 10^{-10}\text{ m} \), what is the total atomic volume in \( \text{m}^3 \) of a mole of hydrogen atoms if the size of a hydrogen atom is about \( 0.5\text{ \AA} \)?

  1. A
    \( 3.15 \times 10^{-7}\text{ m}^3 \)
  2. B
    \( 3.15 \times 10^{-6}\text{ m}^3 \)
  3. C
    \( 6.28 \times 10^{-7}\text{ m}^3 \)
  4. D
    \( 1.05 \times 10^{-7}\text{ m}^3 \)
View Answer & Solution

Correct answer · Option A

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

Explanation

Volume of one atom = \( \frac{4}{3}\pi r^3 = \frac{4}{3} \times \frac{22}{7} \times (0.5 \times 10^{-10})^3 \). Total atomic volume for 1 mole = \( N_A \times \text{Volume of one atom} \approx 3.15 \times 10^{-7}\text{ m}^3 \).
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