Question

What is the ratio of the velocities of CH₄ and O₂ molecules so that they are associated with de-Broglie waves of equal wavelengths?

Answer 1

Answer:

2:1 is the required ratio.

Explanation:

De-Broglie's wavelength = h/mv

Mass of CH₄ = 16 g.

Mass of O₂ = 32 g.

Since, the wavelength is equal,

h / Mass of CH₄ * Velocity of CH₄ = h / Mass of O₂ * Velocity of O₂

h and h get canceled. ("h" is known as Planck's constant)

1 /  Mass of CH₄ * Velocity of CH₄ = 1 / Mass of O₂ * Velocity of O₂

Velocity of CH₄ / Velocity of O₂ = Mass of O₂ / Mass of CH₄

Velocity of CH₄ / Velocity of O₂ = 32 / 16

Velocity of CH₄ / Velocity of O₂ = 2 / 1

Therefore the ratio Velocity of CH₄ : Velocity of O₂ = 2 : 1.