What Is the Ground State Energy of a Particle in a Box?

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SUMMARY

The ground state energy of a particle confined in a one-dimensional box is determined using the formula E_n=(n^2 h)/(8mL^2). In this discussion, the energies EA=4eV and EB=9eV are provided, with the ground state energy calculated as E1=1eV, equivalent to 1.6 x 10-19 J. The relationship between the energy states is clarified, where E2 is identified as 4eV, corresponding to the second energy level (n=2), confirming E1 as 1eV.

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  • Knowledge of energy quantization
  • Proficiency in using the Planck constant (h) and mass (m) in calculations
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szamito
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[SOLVED] Find the ground state energy

1. A particle is confined to a one dimensional box. Two possible state functions and the corresponding energies for the particles are shown in the figure. Find the ground state energy.

EA=4eV

EB=9eV


Homework Equations



E_n=(n^2 h)/(8mL^2 ); E_1=h/(8mL^2 ) then E_n=n^2 E_1

The Attempt at a Solution



E2 =4eV=22E1 then E1=1eV=1,6*10-19 J
 

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szamito said:
...

The Attempt at a Solution



E2 =4eV=22E1 then E1=1eV=1,6*10-19 J

okay, yes. And apparently by "22" you mean [itex]2^2[/itex].
 

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