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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?
Solution
Data: λ1 = λ2, v1 = 4v2
λ = `"h"/"p" = "h"/"mv"`
∴ `lambda_1 = "h"/("m"_1"v"_1), lambda_2 = "h"/("m"_2"v"_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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