Particle box model what am i missing?

[phys-lexic]

1. 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 1x10^-14m. What is the ground state energy of the confined neutron? **the answer it wants is in MeV***



2. equation for the minimum possible energy (ground state; n=1)... E=(h²)/(8mL²)
>h=6.63e^-34 Js
>I use 1x10^-14m as L (is that right)

3. i should be able to just plug in the values and get the answer, but it does not work. after plugging my values in (using 1x10^-14m as L) i get 3.29e^-13, which doesn't work. then i tried converting it to MeV by dividing by 1.6e^-19 (convert J to eV) then dividing again by 10⁶ (converts to Mega) which gives me 2.1, but that doesn't work either... what am i missing?

 

[jbsteele]

The answer you are looking for is 2.07 MeV. To get this, you need to convert the units of h (which is in J⋅s) to eV⋅s by multiplying it by 1.6e-19 J/eV, and then multiply by 106 eV/MeV to convert to MeV. After doing this, you can plug in the values into the equation for the ground state energy and get the answer of 2.07 MeV.

 

[nlightner]

It seems like you are missing the conversion factor for converting eV to MeV. When you divide by 1.6e-19, you are converting J to eV, but to convert eV to MeV, you need to divide by 1e6 (not 106). So the final conversion should be dividing by 1.6e-13. This will give you the correct answer in MeV. Additionally, make sure you are using the correct value for the mass of a neutron (1.674e-27 kg) in the equation.