To increase the de Broglie wavelength of an electron from 0.5×10⁻¹⁰ m to 10⁻¹⁰ m, its energy should be .

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(4) decreased to one-fourth. Given: λ₁ = 0.5×10⁻¹⁰ m and λ₂ = 10⁻¹⁰ m, so the wavelength must double. Idea: λ = h/p = h/(√2mK), so for the same electron K ∝ 1/(λ²). (K₂)/(K₁) = ((λ₁)/(λ₂))² = ((0.5)/1)² = 1/4 Doubling the wavelength needs one-fourth of the energy. So the energy should be decreased to one-fourth.

To increase the de Broglie wavelength of an electron from 0.5×10⁻¹⁰ m to 10⁻¹⁰ m, its energy should be ______.

Step-by-step solution

Why the other options are wrong