#### 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`

Is there an error in this question or solution?

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