Problem about uncertainty principle

[Andurien]

We have an electron pulse of width 1 nanosecond and with kinetic energy of 1keV. We have to calculate Δx and Δp.

I have a question regarding this problem. If they give us the kinetic energy of the electron pulse then we know exactly the momentum right? And so the uncertainty of momentum would be 0 and therefore Δx=∞ for the uncertainty principle ΔxΔp≥h. However I feel this reasoning is incorrect otherwise the problem would be trivial.

 

[mfb]

The momentum, together with the energy, have some small uncertainty (<<1 keV). You can calculate the minimal uncertainty of this, based on the position uncertainty.

 

[Andurien]

And how do I calculate the position uncertainty? Both Δx and Δ p are unkown.

 

[mfb]

Δx is known. It is hidden in the "length" of 1ns, and you can calculate the velocity.

 

[Andurien]

Thank you I finally solved I didn't understand the meaning of that 1ns.