2. Please use the PhET simulation accessible from iCollege to answer the following questions about quantum mechanical tunneling (https://phet.colorado.edu/sims/cheerpj/quantum- tunneling/latest/quantum-tunneling.html?simulation=quantum-tunneling) Quantum Tunneling and Wave Pack ile Colors Help - Total Energy - Potential Energy Configure Energy-. Potential: barrier/well _JL 1.01 Show energy values Show reflection and 0.00 transmission probabilities Energy (ev) Electron Wave Function view. - 0.5 real part - -1.01 imaginary part - magnitude - 2 Te phase 0 0WWII 2TY Direction of incoming wave: Wave Function Electron Wave Function form: O wave packet plane wave coming/Reflected waves: . sum separate Reset All Probability Density 9 10 11 12 Make Quantum Measurement Position (nm ) 11317.5 15 145 1 17 Help! Consider a beam of free particles (represented by a plane wave with total energy E=0.5 ev) impinging on a potential barrier with potential energy U=0.65 eV. Set the width of the barrier to 1 nm. 2.1 What fraction of particles will be reflected by the barrier? What fraction will tunnel through the barrier? Explain how it is possible for part of the QM particles to reach the region on the right-hand side of the barrier? [10 points] 2.2 Explain what happens to the wavefunction in the barrier region if a) the total energy E is decreased to 0.2 ev; or b) the total energy E is increased to 0.8 ev keeping the height of the barrier the same. Produce screenshots for these two cases. [10 points] 2.3 What happens to the fraction of particles that tunnel through the barrier if the width of the barrier is increased from 1 nm to 1.2 nm? Produce a screenshot for the case of 1.2 nm width. Could you relate this observation to the principle of scanning tunneling microscopy? Explain. [15 points]