Debroglie Wavelength Homework: Proton and Alpha Particle Ratio

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Homework Statement

The momentum of a proton and an alpha particle are equal. The mass of alpha particle is 4 times the mass of proton. The ratio of wavelength associated with them is ----

Homework Equations

[tex]\lambda[/tex] = h / p

The Attempt at a Solution

if the momentum are equal then the ratio of wavelengths is 1 / 1. But if i proceed with the formula momentum = m * v keeping m₁ as mass of proton and m₂ as mass of alpha particle i got the equation m₁v = m₂v
Then m₁v = 4m₁v, from debroglie equation, mv = h/[tex]\lambda[/tex], i got h/[tex]\lambda[/tex]₁ = 4h/[tex]\lambda[/tex]₂ which leads to [tex]\lambda[/tex]₂=4[tex]\lambda[/tex]₁. so [tex]\lambda[/tex]₁/[tex]\lambda[/tex]₂ = 1/4. So which one is correct whether 1/1 or 1/4. Please help

 

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. The correct answer is 1/4. Momentum is equal for both particles, but momentum is mass times velocity so the velocity of the alpha particle must be four times that of the proton for them to have equal momentum. Therefore, the wavelength of the alpha particle must be one-fourth of the wavelength of the proton for them to have equal momentum.