A proton 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