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Matter Waves

What should b...

Question

What should be the ratio of velocities of $C H_{4}$ and $O_{2}$ molecules so that they are associated with de Brogile waves of equal wave lenghs ?
According to be Broglie equation = $λ = \frac{h}{m v}$

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Solution

$λ_{C H_{4}} = \frac{h}{(m v)_{C H_{4}}} = \frac{h}{16 \times v_{C H_{4}}}$
$λ_{O_{2}} = \frac{h}{(m v)_{O_{2}}} = \frac{h}{32 v o_{O_{2}}}$
Since $> C H_{4} => O_{2}$
$\Rightarrow \frac{h}{16 v_{C H_{4}}} = \frac{h}{32 v_{O_{2}}} \Rightarrow \frac{v_{C H_{4}}}{v_{O_{2}}} = \frac{32}{16} = \frac{2}{1}$

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