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