Answer to Question #171167 in Atomic and Nuclear Physics for Wandile Manyatsi

Question

Use the uncertainty principle to show that a nucleon which is confined to a region of the order

of ∆x ≈ 1 × 10^−13 cm must have a velocity of the order of 6 × 10^9

cm/s and a kinetic energy

of the order of 20 MeV.

Answer 1

According to the uncertainty principle:

$$KE=\frac{9\hbar^2}{2m\Delta x^2}\approx190\text{ MeV}.$$

The velocity would be

$$\Delta v=\sqrt{\frac{2KE}{m}}\approx190·10^6\text{ m/s}.$$