#### Question

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

#### Solution

The de Broglie wavelength of a particle is given by

`lambda=12.27/sqrtV `Å

Here, *V* is the accelerating potential of the particle.

It is given that

⇒12.27Vproton=12.27Valpha" role="presentation" style="position: relative;">⇒12.27Vproton=12.27Valpha

λproton=λalpha

`=>12.27/sqrt(V_"proton")=12.27/sqrtV_"alpha"`

`=>V_"proton"/V_"alpha"=1`

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Solution A Proton and an α-particle Have the Same De-broglie Wavelength. Determine the Ratio of Their Accelerating Potentials Concept: de-Broglie Relation.