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प्रश्न
The de Broglie wavelengths associated with an electron and a proton are the same. What will be the ratio of (i) their momenta (ii) their kinetic energies?
उत्तर
Data: λ (electron)= λ (proton)
m (proton)= 1836 m (electron)
(i) λ = `"h"/"p"` As λ (electron) = λ (proton),
`("p"("electron"))/("p"("proton")) = 1`, where p denotes the magnitude of momentum.
(ii) Assuming v « c,
KE = `1/2"mv"^2 = 1/2 ("m"^2"v"^2)/"m" = "p"^2/(2"m")`
`("KE"("electron"))/("KE"("proton")) = ("m"("proton"))/("m"("electron"))` = 1836 as p is the same for the electron and the proton.
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