Question

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Neutrons can be produced at low temperatures to serve as probes of molecular structure. When the de Broglie wavelength of a neutron is on the order of the dimensions of chemical bond lengths, the diffraction patterns are especially important for molecular structure. If the speed of a thermal neutron is given by the expression v = (3k_BT/m)^1/2, at what temperature will neutrons have a de Broglie wavelength of 50 pm = 0.5 times 10^-10 m = 0.5 A? Two narrow slits separated by 0.10 mm are illuminated by light of wavelength 600 nm. What is the angular position of the first maximum in the interference pattern? If a detector is located 1.00 m beyond the slits, what is the distance between the central maximum and the first local maximum? If we locate an electron in a hydrogen atom within 10^-3 pm (1 Fermi), calculate the uncertainty in the electron's momentum and its kinetic energy. How does the uncertainty in kinetic energy compare with the ionization energy of the hydrogen atom? What does this result actually mean in terms of finding the electron in the nucleus of a stable hydrogen atom?

Answer 1

v= M2 h 6.626x10-*mKgs-1 n = 1.6 × 10-27Kg λ=0.5×10-10 m K,-138x10-BJK" after substituting all thesevalues T-2809 kelvin