Neutrons and protons in atomic nuclei are confined within a region whose diamete

Question

Neutrons and protons in atomic nuclei are confined within a region whose diameter is 10?15 m.

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

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

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

MeV

PLEASE show work. For part C I have tried 0.0028 MeV and 197.3MeV and 196.79 MeV but none of those are correct. Please help1

Explanation / Answer

Ok so I will do everything in one dimension. Working with a proton(the work would be similar for a neutron)

a.)
?x*m?v ? 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.)
A proton(I know it asks for E of a neutron but if I can do this general calculation then a neutron won't be much different) will have a minimum kinetic energy of

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

c.)
Is the same stuff except I'm dealing with an electron.

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