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If the de Broglie wavelengths associated with a proton and an α-particle are equal, then the ratio of velocities of the proton and α-particle will be - [JEE-Main On line-2018]

1. 1 : 4
2. 1 : 2
3. 4 : 1
4. 2 : 1

Correct answer: 4 : 1

Solution

The de Broglie wavelength is inversely proportional to momentum, which is the product of mass and velocity. Since an α-particle has four times the mass of a proton, for their wavelengths to be equal, the velocity of the proton must be four times that of the α-particle, resulting in a velocity ratio of 4:1.

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