Which of the following factors influences the ratio of De-Broglie wavelengths for gases?

The ratio of De-Broglie wavelengths for gases is significantly influenced by molecular weight and temperature. The De-Broglie wavelength is given by the formula λ = h / (mv), where h is Planck's constant, m is mass (which relates to molecular weight), and v is the velocity of the particles.

When considering different gases at a given temperature, the average kinetic energy of the gas molecules is related to temperature. As temperature increases, the kinetic energy and velocity of the gas molecules also increase, which in turn decreases the De-Broglie wavelength because the wavelength is inversely proportional to momentum (mass times velocity).

In the context of molecular weight, gases with different molecular weights will have different velocities at the same temperature due to the relationship between mass and velocity in achieving the same kinetic energy. This differential in mass and resultant velocities directly impacts the relative De-Broglie wavelengths of the gases, as lighter molecules will exhibit longer wavelengths than heavier ones, assuming similar thermal energy.

This interplay between molecular weight and temperature thus gives rise to distinct De-Broglie wavelengths, making these two factors crucial in determining the ratio of wavelengths across different gases.