Uncertainty principle - just want to check my method

[quantumlolz]

Homework Statement

Estimate the kinetic energy of a constituent quark of mass 300 MeV/c^2 confined insdide a proton of radius 1 fm

Homework Equations

Heisenberg's uncertainty principle $$\Delta x \Delta p \approx \hbar$$ (1)
Kinetic energy $$T=\frac{p^2}{2m}$$ (2)

The Attempt at a Solution

So we've got $$\Delta x$$. So we can rearrange (1) to get $$\Delta p$$

Then we need to use (2). Is it OK to just say $$\Delta T = \frac{\Delta p^{2}}{2m}$$

Alternatively could we use the relation that delta T = dT/dp delta p but then we'd need to know p as well. And how would we then use this to get T?

This should be easy, but I never know when to use the second method using differentiation and when not to. Cheers.

 

[CanIExplore]

Homework Statement

Estimate the kinetic energy of a constituent quark of mass 300 MeV/c^2 confined insdide a proton of radius 1 fm

The Attempt at a Solution

So we've got $$\Delta x$$. So we can rearrange (1) to get $$\Delta p$$

Then we need to use (2). Is it OK to just say $$\Delta T = \frac{\Delta p^{2}}{2m}$$

That is perfectly fine.