Q2. Hydrogen atom Lets have a non-relativistic description of the hydrogen atom using pointlike electron and nucleus without any spin. a. What are the quantum numbers and their range of values of the energy levels? Which energy levels are degenerate?
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- 15 b. Suppose an electron is in a spin state given by x = A(). 8i Find i. the normalization constant A ii. (S.) iii. (S.) and iv. the probability that a measurement of S, will yield h/2.3. What are K,L and M lines you discovered in the Moseley's law experi- ment ? 4. What is the Duane Hunt maximum x-ray frequency of a excitation voltage V = 6kV ? 5. Draw a basic shape of the x-ray absorption spectrum of a generic element, denote the Band a lines along with Duane-Hunt cutoff1. Enumerate the microstates of p3. Determine the MS and ML values for each microstate. 2. On a table of possible MS and ML values, tally the microstates in no. 1 for a particular combination of MS and ML 3. Based on the table in no. 2, determine the atomic term symbols for the allowed atomic states of p3 resulting from the coupling of orbital and spin angular momentums. 4. Arrange the term symbols in no. 3 according to increasing energy.
- 4. An H-atom is in is state. a. What is the probability that the electron is found in sphere given by r ≤ ao b. What is (r) ? c. calculate ().2. Consider the states of hydrogen atom given by (n, l, m) where n a. What is the maximum value of l? If L² is measured what is the maximum possible value that can be obtained? b. What is the maximum value of L₂?In the picture are two diagrams of the first five orbits in the Bohr model labeled A - E. The dot in an orbit is the electron. The nucleus is not shown. Shown is a BEFORE and AFTER state of the atom. An energy level diagram for the Bohr hydrogen atom is shown. Which of these events has occurred in going from the BEFORE to the AFTER state? a. a photon of energy 0.97 eV has been emitted b. a photon of energy 1.51 eV has been absorbed c. a photon of energy 1.51 eV has been emitted d. an electron of energy 1.51 eV has been emitted e. a photon of energy 0.97 eV has been absorbed
- 4. In describing the atom, we often refer to the "electron cloud." Does this mean that the electron is spread out in space in the form of a cloud? Just what is that cloud? In hat ratio would vou expet Ma and Clto combine? ? Why?4. The energy of the atom is in part determined by the electrical potential energy of the electron interacting with the proton nucleus, and when the electron is close to the nucleus it is very tightly bound. That's why the energy is negative, and larger in magnitude the smaller n. What does this tell you about the size of the atom for large n? Explain your reasoning.Which of the following would be closer to the nucleus? a. The ground state (n = 1) of an electron in a singly-charged helium atom. That is, a helium atom with only one electron instead of two. b. Both of these are the same distance from the nucleus c. The ground state electron for the hydrogen.