To increase the de Broglie wavelength of an electron from 0.5×10⁻¹⁰ m to 1×10⁻¹⁰ m, its energy should be .

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(4) decreased to one-fourth. Given: λ₁ = 0.5×10⁻¹⁰ m and λ₂ = 1×10⁻¹⁰ m, so λ₂ = 2λ₁. Idea: λ = h/p = h/(√2mK), so K = (h²)/(2mλ²) ∝ 1/(λ²). (K₂)/(K₁) = ((λ₁)/(λ₂))² = (1/2)² = 1/4 So the energy must be decreased to one-fourth of its value.

To increase the de Broglie wavelength of an electron from 0.5×10⁻¹⁰ m to 1×10⁻¹⁰ m, its energy should be ______.

Step-by-step solution

Why the other options are wrong