JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Atomic Structure

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The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is ______. (Nearest Integer)
(Mass of electron is

9.1 \times 1 0^{- 31} kg

and mass of neutron is

1.6 \times 1 0^{- 27} kg

)

Answer: 1758

Solution

Using de Broglie's relation: λ = h/(mv). For equal wavelengths: λₑ = λₙ, so h/(mₑvₑ) = h/(mₙvₙ). This gives vₑ = (mₙ/mₑ)vₙ. Substituting: vₑ = (1.6 × 10⁻²⁷)/(9.1 × 10⁻³¹) × vₙ = 1758.24 × vₙ. Therefore, x = 1758 (nearest integer).

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Integer answer

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