Particle in a box: You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10^-18 J. What should be the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg) A) 0.11 nm B) 0.22 nm C) 0.15 nm D) 0.18 nm

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Quizplus · Accepted Answer

The ground state energy of a particle in a box is given by:$$E_1 = \frac{h^2}{8mL^2}$$where h is Planck's constant, m is the mass of the particle, and L is the length of the box.We can rearrange this equation to solve for L:$$L = \sqrt{\frac{h^2}{8mE_1}}$$Plugging in the given values, we get:$$L = \sqrt{\frac{(6.626 	imes 10^{-34} 	ext{ J s})^2}{8(9.11 	imes 10^{-31} 	ext{ kg})(5.0 	imes 10^{-18} 	ext{ J})}} = 0.11 	ext{ nm}$$Therefore, the length of the box should be 0.11 nm.

Particle in a Box: You Want to Confine an Electron