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Question:

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

Solution:

i) The relation between de Broglie wavelength λ and accelerating potential V is given by λ=h√(2mqV) So, λp/λα=√((mα/mp)(qα/qp)(Vα/Vp)) Here, λα=λp, mα/mp=4/1, qα/qp=2/1 Thus, 1=√(4)(2)(Vα/Vp) or Vp/Vα=8/1 ii) Also , λ=h/p=h/mv Thus, λp/λα=(mα/mp)(vα/vp) or 1=(4)(vα/vp) or vp/vα=4/1