If a particle in a box has a ground-state energy of 10.0 eV,what is the energy of the 4^th excited state? A) 20.0 eV B) 40.0 eV C) 160 eV D) 50.0 eV E) 250 eV

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Quizplus · Accepted Answer

The energy levels of a particle in a box are given by the equation: E = (n^2*h^2)/(8*m*L^2), where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the box. For the ground-state energy (n=1), we have: 10.0 eV = (1^2*h^2)/(8*m*L^2) For the 4^th excited state (n=7), we have: E = (7^2*h^2)/(8*m*L^2) = 49*(h^2)/(8*m*L^2) Taking the ratio of the two equations, we get: E/10.0 eV = (49*(h^2)/(8*m*L^2))/((h^2)/(8*m*L^2)) Simplifying, we get: E = 490.0 eV Therefore, the best choice is E) 250 eV, which is the closest option to the calculated energy value.

If a Particle in a Box Has a Ground-State Energy