What is the ratio of De-Broglie wavelengths for helium to hydrogen at room temperature?

The ratio of De-Broglie wavelengths for two gases can be derived from the formula for the De-Broglie wavelength, which is given by:

[

\lambda = \frac{h}{p}

]

where ( \lambda ) is the De-Broglie wavelength, ( h ) is Planck's constant, and ( p ) is the momentum of the particle. The momentum ( p ) of a particle is related to its mass ( m ) and velocity ( v ) by the equation:

[

p = mv

]

At a given temperature, the average kinetic energy of gas particles is related to the temperature by:

[

KE = \frac{3}{2} kT

]

where ( k ) is Boltzmann's constant and ( T ) is the temperature in Kelvin. The mean speed ( v ) of gas molecules is also dependent on their molar mass ( M ):

[

v = \sqrt{\frac{3kT}{M}}

]

Combining these equations, we find that the De-Broglie wavelength can be expressed in terms of mass:

[

\lambda \propto \frac{1}{