Answer:
The de-Broglie wavelength of the nitrogen molecule is 0.0272 nm
Explanation:
The mass, m, of the nitrogen molecule, N₂ = 14.0076u = 28.0152 × 1.66 × 10⁻²⁷ kg
[tex]v_{rms}[/tex] of N₂ = 523 m/s
The de-Broglie wavelength is given as follows;
[tex]de-Broglie \, wavelength = \dfrac{h}{m\times v_{rms}}[/tex]
Where:
h = Planck's constant = 6.62607004 × 10⁻³⁴ m²·kg/s
Plugging in the values, we have;
[tex]de-Broglie \, wavelength = \dfrac{6.62607004 \times 10^{-34}}{28.0152 \times 1.66 \times 10^{-27}\times 523} = 2.72\times 10^{-11} \, m[/tex]
Hence, the de-Broglie wavelength of the nitrogen molecule = 0.0272 nm.
