The de Broglie wavelength of an oxygen molecule at is . The value of is (take Planck’s constant , Boltzmann constant , mass of oxygen molecule ). [2026]

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Solution

Q.
The de Broglie wavelength of an oxygen molecule at $27 ° C$ is $x \times 10^{- 12} m$ . The value of $x$ is (take Planck’s constant $= 6.63 \times 10^{- 34} J.s$ , Boltzmann constant $= 1.38 \times 10^{- 23} J/K$ , mass of oxygen molecule $= 5.31 \times 10^{- 26} kg$ ). [2026]

1 20

2 30

3 26

4 24

Ans.
(3)

$λ = \frac{h}{\sqrt{2 m K}} = \frac{h}{\sqrt{2 m (\frac{3}{2} k T)}}$

$λ = \frac{h}{\sqrt{3 m k T}}$

$= \frac{6.63 \times 10^{- 34}}{\sqrt{3 \times 5.31 \times 10^{- 26} \times 1.38 \times 10^{- 23} \times 300}}$

$= 2.58 \times 10^{- 11} = 25.8 \times 10^{- 12}$

$So, x = 26$

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