Question

A proton and a Li³⁺ nucleus are accelerated by the same potential. If λ_Li and λ_P denote the de Broglie wavelengths of Li³⁺ and proton respectively, then the value of `λ_("Li")/(λ_"P")` is x × 10⁻¹. The value of x is ______. [Rounded-off to the nearest integer]

[Mass of Li³⁺ = 8.3 mass of proton]

Options

• 1

• 2

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• 4

Answer 1

A proton and a Li³⁺ nucleus are accelerated by the same potential. If λ_Li and λ_P denote the de Broglie wavelengths of Li³⁺ and proton respectively, then the value of `λ_("Li")/(λ_"P")` is x × 10⁻¹. The value of x is 2.

Explanation:

From the de-Broglie wavelength, we get

λ = `"h"/(sqrt(2"meV"))`

∴ `λ_("Li"^(3+))` = `"h"/(sqrt(2"m"_("Li"^(3+))"eV"))`;

λ_P = `"h"/(sqrt(2"m"_"P""eV"))`

By the problem, `"V"_("Li"^(3+))` = V_P

`"m"_("Li"^(3+))` = 8.3 m_p

∴ `λ_("Li"^(3+))/(λ_"P") = sqrt("m"_"P"("e") xx "V")/(sqrt(8.3 "m"_"P" xx 3"e" xx "V"))`

= `1/sqrt(8.3 xx 3)`

= `1/5`

= 0.2

= 2 × 10⁻¹