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Question:

If the de Broglie wavelengths associated with a proton and an α-particle are equal, then the ratio of velocities of the proton and the α-particle will be:

1:4

2:1

4:1

1:2

Solution:

The correct option is C 4:1
Given de Broglie Wavelength λp=λα
So, h/mp × vp = h/mα × vα
vp/vα = mα/mp = 4mp/mp
Because Mass of α particle is 4 times mass of proton.
So 4:1.
Option C is correct answer