Minimum Kinetic Energy of a Proton Confined in a Uranium Nucleus

[Shackleford]

36. A proton is confined in a uranium nucleus of radius 8 x 10^-15 m. Determine the proton's minimum kinetic energy according to the uncertainty principle if the proton is confined to a one-dimensional box that has length equal to the nuclear diameter.

What's wrong with my equation and value I used for L^2?

 

[nickjer]

You defined $$L = 2\Delta x$$ so that means L should be the diameter and not the radius of the nucleus.

 

[Shackleford]

You defined $$L = 2\Delta x$$ so that means L should be the diameter and not the radius of the nucleus.

Son of a... It does say diameter. And so delta-x is the radius.

Where did the 8 come from?

 

[nickjer]

I think the 8 came from if you pulled the 2 from 2*r out of the square it would be 4. And then you would have 2*4 = 8.

 

[Shackleford]

But the 1.6 x 10^-5 nm = 2r, so that term is already squared. She has 8*m*d^2, not 2*m*(2r)^2 which would be 8*m*r^2.

The definition of delta-x is arbitrary, right? But it has to make sense in the context of the wave function. It seems that delta-x = L/2 is a common definition.

 

[nickjer]

I think your grader just corrected it twice. Not thinking that you would interpret at as a single correction.