a nonrelativistic proton is confined to a length of 2.0 pm on the x-axis. what is the kinetic energy of the proton if its speed is equal to the minimum uncertainty possible in its speed

K = 1.29eV

Explanation:

In order to calculate the kinetic energy of the proton you first take into account the uncertainty principle, which is given by:

     (1)

Δx : uncertainty of position = 2.0pm = 2.0*10^-12m

Δp: uncertainty of momentum = ?

h: Planck's constant = 6.626*10^-34 J.s

You calculate the minimum possible value of Δp from the equation (1):

The minimum kinetic energy is calculated by using the following formula:

      (2)

m: mass of the proton = 1.67*10^{-27}kg

in eV you have:

The kinetic energy of the proton is 1.29eV

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