What Is the Correct Ground State Energy of a Neutron in a Box?

AI Thread Summary
The discussion revolves around calculating the ground state energy of a neutron confined in a one-dimensional box using the particle in a box model. The formula used is En = h^2/8mL^2, where users are attempting to substitute the values for Planck's constant, mass of the neutron, and the box length. A participant initially calculates the energy but realizes their answer is incorrect, prompting inquiries about unit conversion to MeV. It is clarified that the conversion from joules to MeV requires multiplying by 6.24e12, but even after this adjustment, the participant continues to struggle with obtaining the correct answer. The thread highlights the importance of proper unit conversion in quantum mechanics calculations.
wayneinsane
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Homework Statement



The particle in a box model is often used to make rough estimates of ground state energies. Suppose that you have a neutron confined to a one-dimensional box of length equal say 1 x 10^-14m. What is the ground state energy of the confined neutron?

answer in MeV?



Homework Equations



En = h^2/8mL^2



The Attempt at a Solution



I am getting the wrong answer... I am getting:

(6.626e-34)^2/((8)(1.675e-27)(1e-14)^2) = 3.28e-13

That is wrong... anyone?
 
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Do you know the actual answer? Are you expressing it in MeV?
 
I don't have the answer, I have to submit electronically and I am getting it wrong.

I'm not sure actually...that was my issue...maybe I am not converting to MeV. Any ideas?
 
Remember, Planck's constant that you applied is in J*S. Thus your units is in joules. Convert your answer to MeV :)
 
Well, I multiplied my answer by 6.24e12 because 1J = 6.24e12MeV, and I got 2.05, that is still wrong.
 
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