Neutrons and protons in atomic nuclei are confined within a

Neutrons and protons in atomic nuclei are confined within a region whose diameter is 10¹⁵ m.

(a) Using Heisenberg\'s uncertainty principle, at any given instant, what is the minimum speed an individual proton or neutron can be moving?

answer = ??? c

(b) What is the approximate kinetic energy of a neutron that is localized to within such a region?

answer= ??? Mev

(c) What would be the corresponding energy of an electron localized to within such a region?

answer= ??? Mev

note the particle is moving with a speed relative to the speed of light

Solution

x*mv h/(4)

v h/(4*m*x)

v 6.626E-34/(4*1.67E-27*1E-15)

So the minimum speed for a proton confined to that particular space will be = 31573672.2 m/s or 31573.6722 km/s or 31.5736722 Mm/s
b) E = (1/2)mv^2

E = (1/2)(1.67E-27)(31573672.2)^2 = 8.324E-13 joules of energy