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A proton and an a-particle have the same de-Boglie wavelength. Determine 

the ratio of (i) their accelerating potentials and (ii) their speeds.           (2 marks)

Explanation:

(i) λ=h2mqVV=h22mqλ2                                (1/2 mark)

mα=4mp, qα=2qpVpVα=mαqαmpqp=4mp×2qpmpqp=8:1                                              (1/2 mark)

(ii) λ=hmv v=h                                     (1/2 mark)

VpVα=mαmp=4                                             (1/2 mark)

 

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