Aproton is confined in a uranium nucleus of radius 7.2x10-15 m. determine the proton’s minimum kinetic energy according to the uncertainty principle if the proton is confined to a 1 dimensional box that has the length of the nuclear diameter. you can assume that the velocities involve are non-relativistic, so that ekin=p2 /(2m).

  K = 16.1 10⁻¹⁵ J

Explanation:

The equation for the uncertainty principle establishes the relationship between the medical minimum that can simultaneously perform the position and momentum of a particle.

      ΔxΔp> = (h/2π) / 2

Let's calculate the variation of the moment

     Δp> = (h/2π) / 2 Δx  

     Δp> = 6.63 10⁻³⁴ / (4π  7.2 10⁻¹⁵)

     Δp = 7.33 10⁻²¹ m / s

Let's calculate the kinetic energy

     K = p² / 2m

     K = (7.33 10⁻²¹)² /2 1.67 10⁻²⁷

     K = 16.1 10⁻¹⁵ J

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