Determine the most probable distance from the nucleus for an electron in the 2p orbital of a hydrogen atom. The radial wavefunction, R (r), for the 2p orbital is given by 1 R21 (r) = Zr e 2a0 Zr 2 /6 \ ao ao Give your answer in terms of ao.
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- Draw to careful scale an energy-level diagram for hydrogen for levels with n=1, 2, 3, 4, inf. Show the following on the diagram: (a) the limit of the Lyman series, (b) theHb line, (c) the transition between the state whose binding energy (= energy needed to remove the electron from the atom) is 1.51 eV and the state whose excitation energy is 10.2 eV, and (d) the longest wavelength line of the Paschen series.For the hydrogen atom in the 4d excited state find the possible values of n,l,m,m,, and mj. Give the term notation for each possible configuration.While studying the spectrumn of a gas doud in space, an astronomer magnifies a spectral line that results from a transition from a p state to an s state, She finds that the line at 575.050 nm has actually split into three lines, with adjacent lines 4.70 x 10- nm apart, indicating that the gas is in an external magnetic field. (Ignore effects due to electron spin.) What is the strength of the external magnetic field? O B=3.25 T OB-2.98 T O B=2.79 T O B=3.05 T OB=2.05 T
- I need help with the last 3.: Write out the electronic configuration of the ground state for fluorine (Z = 9). 015²25²2pl 15²2522p³ 15²25²2p4 O 16²25²2p5The radial probability density of a hydrogen wavefunction in the 1s state is given by P(r) = |4rr2 (R13 (r))²| and the radial wavefunction R1s (r) = a0 , where ao is 3/2 the Bohr radius. Using the standard integral x"e - ka dx n! calculate the standard deviation in the radial position from the nucleus for the 1s state in the Hydrogen atom. Give your answer in units of the Bohr radius ao.
- Problem 3: Calculate the energy changes corresponding to the transitions of the hydrogen atom. Give all your answers in eV. Part (a) From n = 3 to n = 4. Part (b) From n = 2 to n = 1. Part (c) From n = 3 to n = ∞.Sketch the energy levels of the hydrogen atom including the fine structure, upto n=3. Show the possible transitions. How many different lines are there?e. The radial function for the 3s orbital in the hydrogen atom is given below: 3/2 (27 – 180 + 202)e (o = ) Zr ao = 52.92 pm R35 = ao. 27 [3ao- Calculate the distance(s) of the node(s) of the 3s orbital of the hydrogen atom from the nucleus.