2. The 4p radial wavefunction for the H-atom is (1/32/15) × g(20 - 10p + p²) x Z3/2 × ep/2 Using this information determine the radius of the nodes in units of Bohr radius for the 4p orbitals.
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- The wavelengths in the hydrogen spectrum with m = 1 form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the series.What wavelength of light is emitted by a hydrogen atom in which an electron makes a transition from the n = 7 to the n = 4 state? Enter this wavelength expressed in nanometers. 1nm = 1 x 10-9m. Assume the Bohr model.The orbital radii of a hydrogen-like atom is given by the equation What is the radius of the first Bohr orbit in (a) He+,(b) Li2+, and (c) Be3+
- 22:39 Wed 14 Dec Question 2 A hydrogen atom is in the n = 55 state. X (b) Calculate the change in energy for a transition from the n = 55 state to the n = 56 state. (c) Calculate the wavelength of the photon that is absorbed in the transition in (b). @ 4% 7What frequency of light, in THz (Terahertz, or 10^12 Hz), is needed for an electron in a hydrogen atom to go from the n = 2 state to the n = 3 state?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:
- Which of the following lists of quantum numbers for the hydrogen atom (if any) are NOT possible? Circle all that apply and explain why they are not possible.(a) If an electron makes a transition from the n = 7 Bohr orbit to the n = 3 orbit, determine the wavelength of the photon created in the process. nm(b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon is emitted. m/sA hydrogen atom is in its fourth excited state. The atom emits a 1.28E+3nm wavelength photon. Determine the maximum possible orbital angular momentum of the electron after emission. Express your answer as multiples of hbar.