The ground state energy of a particle in a box of width 1.0 * 10^-9 m is 2.10 * 10^-3 eV.What is the mass of the particle? A)1.62 * 10^-28 kg B)2.42 * 10^-27 kg C)6.83 * 10^-27 kg D)1.67 * 10^-27 kg

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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 the Planck constant* $$m$$ is the mass of the particle* $$L$$ is the width of the boxWe can rearrange this equation to solve for the mass of the particle:$$m = \frac{h^2}{8E_1L^2}$$Plugging in the given values, we get:$$m = \frac{(6.626 imes 10^{-34} ext{ J s})^2}{8(2.10 imes 10^{-3} ext{ eV})(1.602 imes 10^{-19} ext{ J/eV})(1.0 imes 10^{-9} ext{ m})^2}$$$$m = 1.62 imes 10^{-28} ext{ kg}$$Therefore, the mass of the particle is 1.62 * 10^-28 kg.

The Ground State Energy of a Particle in a Box