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A Proton and an α-particle Have the Same De-broglie Wavelength Determine the Ratio of Their Speeds. - CBSE (Science) Class 12 - Physics

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Question

A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of  their speeds.

Solution

The de Broglie wavelength (λ) of a particle is also given by

`lambda=h/(mv)`

Here,

h = Planck's constant

m = Mass

v = Speed of the particle

`:.lambda"proton"=h/(m_"proton"v_"proton")`

`lambda"alpha"=h/(_"alpha"v_"alpha")`

λproton=λalpha

`therefore h/(m_"proton"v_"proton")=h/(4m_"proton"v_"alpha")`

`therefore (4h)/h=(m_"proton"v_"proton")/(m_"proton"v_"alpha")`

`therefore 4=(v_"proton")/(v_"alpha")`

`=>(v_"proton")/v_"alpha"=4`

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Solution A Proton and an α-particle Have the Same De-broglie Wavelength Determine the Ratio of Their Speeds. Concept: Wave Nature of Matter.
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