First slide

Quantum mechanical model of the atom

Question

At 200°C,hydrogen molecule have velocity 2.4 × 10⁵ cm s^-1. The de Broglie wavelength in this case is approximately

Moderate

A

$1 Å$
B

$1000 Å$
C

$100 Å$
D

$10 Å$

Solution

$λ = \frac{h}{mv} = \frac{6 .6 \times 10^{- 27} ergs}{\frac{2}{N_{A}} \times 2 .4 \times 10^{5} {cms}^{- 1}}$
$\begin{array}{l} (Mass of 1 molecule of H_{2} = \frac{2}{6.02 \times 10^{23}}) \\ = \frac{6.6 \times 10^{- 27} \times 6.02 \times 10^{23}}{2 \times 2.4 \times 10^{5}} \\ = 8.27 \times 10^{- 9} cm \\ = 0.8 \times 10^{- 8} cm = 0.8 Å \approx 1 Å \end{array}$

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