QJEEM18Ph379b: JEE Main 2018 Physics - Class 12 JEEM18Ph379b Solution: If the de Broglie wavelengths associated with a proton and an α …

Question

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If the de Broglie wavelengths associated with a proton and an

α

-particle are equal, then the ratio of velocities of the proton and the

α

-particle will be :

Accepted Answer

We know,

λ_{p} = \frac{h}{p_{p}}

=

\frac{h}{m_{p} v_{p}}

Similarly,

λ_{α} = \frac{h}{m_{α} v_{α}}

Given,

λ_{p} = λ_{α}

\Rightarrow

\frac{h}{m_{p} v_{p}} = \frac{h}{m_{α} v_{α}}

∴

\frac{v_{p}}{v_{α}} = \frac{m_{α}}{m_{p}}

=

\frac{4 m_{p}}{m_{p}} = \frac{4}{1}

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