V= 8 1. The mass of a neutron is 1.67 × 10-27 kg. Convert this to units of MeV/c²) Calculate the velocity of neutrons required to perform neutron diffraction of a specific crystal, whose interatomic spacing is of the order 2A. What is the total kinetic energy for these neutrons? What is its relativistic energy? 2. From scattering experiments, it is found that the nuclear diameter is of the order of 10-15 m (1 fm). The energy of an electron in ẞ-decay experiment is of the order of a few MeV. Use these data and the uncertainty principle to show that the electron is not a constituent of the nucleus. 3. A free electron has wave function (x,t) = sin(kx - wt). Determine the electron's de Broglie wavelength, momentum, kinetic energy and speed when k = 50 nm 4. Normalize the following wavefunctions (a) (x) = sin (7); for a particle in a 1D box of length L. L (b) (r) = xe−z/2 (c) (x) = (x²/a²)+(ikx) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/L2, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy attractive? for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or 6. Plot qualitative wavefunctions for the scenarios shown below. V=O Z B) -E Vo c) TA 1 그 V=0 Vzvo E v(x) 0,02