Question

Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an α-particle, what are the possibilities for the other particle?

Answer 1

Data : λ₁ = λ₂ , v₁ = 4v₂

λ = \(\cfrac{h}p\) = \(\cfrac{h}{mv}\)

∴ λ₁ = \(\cfrac{h}{m_1v_1}\), λ₂ = \(\cfrac{h}{m_2v_2}\)

∴ m₁ = m₂ \(\cfrac{v_2}{v_1}\) = m₂ \((\cfrac{1}4)\) = \(\cfrac{m_2}4\)

As particle 2 is the a-particle, particle 1 (having the mass \(\cfrac{1}4\) times that of the a-particle) may be a proton or neutron.