3. An electron in a hydrogen atom is in the M shell (so n=3).A) What is the smallest orbital angular momentum this electron could have?B) What is the largest orbital angular momentum this electron could have?C) What is the maximum orbital angular momentum that could be measured in anyparticular direction? (This isn't a repeat of (B))!D) How many orbital angular momentum states could this electron have?

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3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:
An electron is known to have an energy level of 5. What are the possible values for its angular momentum quantum numbers? Explain your answer
3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.
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 a H-atom series, the shortest wavelength transition is registered at 821 nm. plsease explain the step by step (1) Identify the transition. (2) Calculate the energy of the above transition in J and eV. (3) What is this series? (4) Calculate the longest wavelength in the series?