(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to...
An electron is confined to a one-dimensional infinite well. From experiment, the first excited state is measured to have an energy 1.2 eV above the ground state. What must be the width of the well?
2) (5 points) A hydrogen atom at rest is in a state of quantum number n=6. The electron jumps to a lower state, emitting a photon of energy 1.13 eV. (a) What is the quantum number of the state to which the electron jumped? (b) What is the ratio of the angular momentum of the electron after the emission of the photon? (c) Estimate the recoil speed of the hydrogen atom due to emission of the photon.
3 (b) The energy of a Bohr atom in the n-th excited state is given by the formula E--a2mc2 2,7, where α-e2/(4πέρ,10hc)-1 /137, m is the electron mass and e denotes the electron electric charge. i) Why is the total energy negative? Explain briefly your answer. ii) What is the radius of the electron in the n-th excited state in the Bohr atom? To answer that correctly follow the next steps Use Bohr's angular momentum quantization principle to obtain an...