The energy of an electron in the ground state of hydrogen atom is - 13.6 eV. Calculate Rydberg's constant and wavelength of the second member of Balmer series.
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A: The mean radius for an orbital is,
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- Normalize the wavefunction for the 2s orbital of a hydrogen electron. 3 Rn. 1 (r) = = (²/7) ² (2 − p) e - ² - a 2Zr naCalculate the wavelength of the third line of the Paschen series for hydrogen.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: