Guidelines for your solutions: Submit your answers on a separate sheet of paper, ensuring your name and the relevant question numbers are clearly indicated. Make sure to keep the order of the questions Always include the correct units for your answers. Before the deadline, upload your solutions as a single PDF file to Canvas using the Adobe Scan app or a similar tool. Solutions will be made available after the submission deadline. The first question is 6 pts, and the rest are 3 pts each Note: Late submissions will not be accepted. 1. Mark the following questions as True (T) or False (F). (No need to write questions with the solutions) a. The photoelectric effect confirms wave-like properties of electromagnetic radiation. b. The quantization of energy means that energy can be discarded or absorbed only in packets as the atom or molecules transition between their allowed energy levels (or states). c. According to the de Broglie relation, only electrons (or similar microscopic particles) can be described based on particle-wave duality. d. For photoelectrons to emit from the metal the frequency of the incident light must be larger than /h e. The superposition of many wavefunctions with constructive interference in one place leads to a well- defined momentum. f. The observable for the system, such as energy or position, can be calculated using the expectation value and a corresponding QM operator. 2. Perform the following calculations regarding an electron: a) Determine the wavelength when the electron is moving at the speed of light. b) If the electron is confined to a box measuring 4 pm, compute the uncertainty in its momentum. 3. The work function of metallic caesium is 2.14 eV. Calculate the kinetic energy and the speed of electrons ejected by the light of a wavelength of 650 nm. 4. Is the function f=2x2+6y2+5z3 eigenfunction of the operator ? 5. Normalize the wavefunction And write down the expression for the normalized wavefunction. 6. Determine whether the function below satisfies the boundary conditions for a particle in a 1D box with a length equals to L.CHEM