A particle is confined in a 1D box (0<x<L). The ratio of the energies of the particle in state n=3 to state n=2 isa.9/4b.1/4c.4
Question
A particle is confined in a 1D box (0<x<L). The ratio of the energies of the particle in state n=3 to state n=2 isa.9/4b.1/4c.4
Solution
The energy of a particle in a 1D box is given by the equation E_n = n^2 * h^2 / (8mL^2), where n is the state, h is Planck's constant, m is the mass of the particle, and L is the length of the box.
For state n=3, the energy E_3 = 3^2 * h^2 / (8mL^2) = 9h^2 / (8mL^2).
For state n=2, the energy E_2 = 2^2 * h^2 / (8mL^2) = 4h^2 / (8mL^2).
The ratio of the energies of the particle in state n=3 to state n=2 is therefore E_3 / E_2 = (9h^2 / (8mL^2)) / (4h^2 / (8mL^2)) = 9/4.
So, the correct answer is a. 9/4.
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