Two particles have the same de Broglie wavelength and one is moving fo

1.	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» 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.

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»

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.