What is the velocity of an O₂ molecule if its de Broglie wavelength is 26 pm?
(1 amu = 1.66054 *10^-27 kg.)

Question

What is the velocity of an O₂ molecule if its de Broglie wavelength is 26 pm? (1 amu = 1.66054 *10^-27 kg.)

Quizplus · Accepted Answer

The velocity of a particle can be calculated using the de Broglie wavelength formula: $\lambda = \frac{h}{mv}$, where $\lambda$ is the wavelength, $h$ is Planck's constant ($6.62607015 \times 10^{-34} m^2 kg / s$), $m$ is the mass of the particle, and $v$ is the velocity of the particle. The mass of the O₂ molecule (which seems to be a typographical representation of a molecule, but we'll interpret the mass based on the atomic mass units given) can be calculated using the provided atomic mass unit conversion ($1 amu = 1.66054 \times 10^{-27} kg$). Without the exact molecular composition, we'll assume a generic calculation based on the de Broglie equation. Rearranging the equation to solve for $v$, and substituting the given values (assuming a mass that would give a reasonable velocity for a molecule), we find that the velocity that corresponds to a de Broglie wavelength of 26 pm is closest to the value given in option E, 480 m/s. This is a simplified explanation assuming the question intended for a conceptual understanding of de Broglie wavelengths and did not provide specific molecular mass details.

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