The ratio of de-Broglie wavelength of an α-particle and a proton accelerated from rest by the same potential is 1/√m. The value of m is:
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The ratio of de-Broglie wavelength of an α-particle and a proton accelerated from rest by the same potential is 1/√m. The value of m is:

G1 Physics · Accepted Answer

For a particle accelerated through the same potential V, λ = h/√(2mqV). Therefore λ(α)/λ(p) = √[m(p)q(p)/(m(α)q(α))]. For an α-particle, m(α) ≈ 4m(p) and q(α) = 2q(p). Hence λ(α)/λ(p) = 1/√8, so m = 8.