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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?
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Solution
Data:
λ1 = λ2,
v1 = 4v2
λ = `h/p = h/(mv)`
∴ `lambda_1 = h/(m_1v_1)`,
`lambda_2 = h/(m_2v_2)`
As λ1 = λ2,
m1v1 = m2v2
∴ `m_1 = (m_2 v_2)/v_1 = m_2 (1/4) = m_2/4`
As particle 2 is the ex-particle, particle 1 (having the mass `1/4` times that of the a-particle) may be a proton or neutron.
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