Question

What should be the ratio of the velocity of `1CH_(4) and O_(2)` molecules so that they are associated with de Broglie wave of equal wavelegth ?

Answer 1

According to de Broglie equation
For methane `(CH_(4))`
`lambda _(CH_4) = (h)/(m_(CH_4) xx v_(CH_4))`
For oxygen `(O_(2))`
`lambda_(O_2) = (h)/(m_(O_2) xx v_(O_2))`
since the wavelength of `CH_(4)` and `O_(2)` sould be equal
`lambda _(CH_4) = lambda _(O_2)`
`or (h)/(m_(CH_4) xx v_(CH_4)) = (h)/(m_(O_2) xx vO_(2))`
`m_(CH_4) xx vCH_(4) = m_(O_2) xx vO_(2)`
`or (vCH_4)/(v_(O_2)) = (m_(O_2))/(m_(CH_4)) = (32)/(16) = 2`