A. 0.500 mol sample of hydrogen is at 300 K . Find the number of molecules having speed between \( 400 \mathrm{~m} \mathrm{~s}^{-1} \) and \( 401 \mathrm{~m} \mathrm{~s}^{-1} \) the mass of hydrogen is \( 1.67 \times 10^{-27} \mathrm{~kg} \) and the Boltzmann constant \( k_{B}= \) \( 1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K} \). And \( \left(N_{A}=6.02 \times 10^{23} \mathrm{~mol}^{-1}\right) \operatorname{Hint}\left(n=\frac{N}{N_{A}}\right) \)
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The distribution function for the speed \( v \) of molecules in an ideal gas is given by: \[ f(v) = 4\pi \left( \frac{m}{2\pi k_B T} \right)^{3/2} v^2 e^{-\frac{mv^2}{2k_B T}} \] where: - \( m \) is the mass of a single molecule, - \( k_B \) is the Boltzmann Show more…
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