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A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3×10⁶ ms⁻¹. The velocity of the particle is:

1. 2.7×10⁻¹⁸ ms⁻¹
2. 9×10⁻² ms⁻¹
3. 3×10⁻³¹ ms⁻¹
4. 2.7×10²¹ ms⁻¹

Correct answer: 9×10⁻² ms⁻¹

Solution

Using the de Broglie wavelength formula, λ = h / (mv), the wavelength of the electron is λ = h / (mₑvₑ). For the particle, λ = h / (mₚvₚ). Equating the two wavelengths and solving for vₚ, we get vₚ = (mₑvₑ) / mₚ. Substituting mₑ = 9.1×10⁻³¹ kg, vₑ = 3×10⁶ ms⁻¹, and mₚ = 1×10⁻³ g = 1×10⁻⁶ kg, we find vₚ = 9×10⁻² ms⁻¹.

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