Particle in a box, some clarification please

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Homework Help Overview

The discussion revolves around the energy of a particle in a one-dimensional box, specifically focusing on the relationship between the quantum number and kinetic energy. Participants are exploring the implications of the energy formula and its interpretation in the context of quantum mechanics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether the energy expression represents total energy or kinetic energy, and how to derive the quantum number from a given kinetic energy value. There are attempts to rearrange the energy formula to solve for the quantum number.

Discussion Status

The discussion is ongoing, with some participants providing clarifications about the relationship between total energy and kinetic energy in the context of the problem. There is acknowledgment of the challenges in obtaining a whole number for the quantum number, indicating a productive exploration of the topic.

Contextual Notes

Participants note that the potential energy is zero within the box, which is a key assumption in this problem. There is also mention of the unrealistic nature of obtaining a whole number for the quantum number given the calculations involved.

rwooduk
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the energy of an n state can be given by:

E = (nh)^2 / 8mL^2

is this a representation of the Kinetic energy of the particle? i thought it was but this question has got me confused.

it asks for the Energy of the n=1 state, which I've done. then it asks what quantum number, n would be needed if the Kinetic Energy was 0.025eV.

i rearranged the above eqn for n and put E= (0.025ev X 1.6x10^-19 ), but get something stupid as a result.

so, is E the energy of the state of the particle OR it's kinetic energy OR both?

Thanks in advance for any help.
 
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Hmm, the energy state is the total energy, but as you only have kinetic energy, it should be straight forward, as you've done.
 
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The potential in the case of particle in a box problem,is zero inside the box and greater than zero outside it.So inside the box,the total energy of the particle is equal to its kinetic energy.
 
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yes this is as i suspected, i get a stupidly high number for n and its not a whole number either! will recalculate.

thanks for the replies!
 
Well, getting a whole number for n is quite unrealistic, when you think about the numbers and decimals, you are using.

Also I don't think there are any limits for the quantum number for a particle in a box.
 

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