[UPSC CSE 2007] Foundations of Quantum Mechanics (Q69, 20M)

(i) State and explain Heisenberg's uncertainty principle. Experimental data reveal that no electron in an atom has energy greater than 4 MeV. Assuming that the radius of a nucleus is 10^{-14}\text{ m}, show using Heisenberg's uncertainty principle that an electron cannot exist inside the nucleus. (10) (ii) Calculate the de Broglie wavelength of thermal neutrons at 300 K. (10)