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A proton and an α–particle are accelerated from rest to the same energy. The de Broglie wavelengths λₚ and λₐ are in the ratio:

1. 4 : 1
2. 2 : 1
3. 1 : 1
4. √2 : 1

Correct answer: 2 : 1

Solution

The de Broglie wavelength is inversely proportional to the square root of the mass for particles with the same kinetic energy. Since the α-particle has four times the mass of the proton, its de Broglie wavelength will be half that of the proton. Thus, the ratio λₚ : λₐ is 2:1.

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