# A Proton and an α-particle Have the Same De-broglie Wavelength Determine the Ratio of Their Speeds. - Physics

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

Concept: Wave Nature of Matter
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