3.1 Calculate the value of r at which the radial probability density of the hydrogen atom reaches its maximum 3.1.1 n=1, 1-0, m=0 3.1.2 I n-1, m=0 Given Rnt(): - - (não) 3/2 (n-1-1)! (22) 2n[(n+1)]³ nao, -T/ndo L₂ 21+1 n+l (27)
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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.-2r/rB dr. Find the probability that the r2e The radial probabiliity density for an electron in the 1s orbital is given by P(r) electron is found between 1.22 rg and (1.22+0.001)r;. Give you answer to two decimal places in exponential notation. Round your answer to 2 decimal places. Add your answerThe energies, E, for the first few states of an unknown element are given in the table in arbitrary units. 71 1 4 CO E -21 -4 -3 ... A gaseous sample of this element is bombarded by photons of various energies in these same units. Match each photon to the result of its absorption, or lack thereof, by an n = 1 electron. Answer Bank Photon Energy Result n=I to n=2 21 n=| to # = 17 n=1 ton= 15 clectian cjecled 12 TI absorbed
- (4) Electronic energy level of a hydrogen atom is given by R ; п %3D 1,2, 3,... n2 E = - and R = 13.6 eV. Each energy level has degeneracy 2n2 (degeneracy is the number of equivalent configurations associated with the energy level). (a) Derive the partition function for a hydrogen atom at a constant temperature. (b) Consider that the energy level of a hydrogen atom is approximated by a two level system, n = 1,2. Estimate the mean energy at 300 K.Use the Rydberg equation to calculate the wavelength (in nm) of the hydrogen Balmer series line having nouter = 5 and ninner = 2. After calculating delta E, take the absolute value, and solve for frequency using Equation (1). Use this frequency in Equation (2) to solve for the wavelength.Express your answer to 3 significant figures.Needs Complete solution with 100 % accuracy don't use chat gpt or ai.Calculate the probability density | W100(r,8,0)|² of finding the electron at the nucleus (considered as a point at the center of coordinates) for a hydrogen atom in the state 100. \3/2 R10(r) =: 2Zr (hbar)? ao = me? Yoo(e,$)= - nao Please notice that the above formulas are written in the cgs system of units, so mass is in grams, distance is in cm, and energy is in erg = g cm2/s2. In this system of units e = 4.8032068 X 10-10 statC, where 1 statC = 1 cm3/2 g1/2 s-1 O 0.18 pm-3 2.15 x 10-6 pm-3 Oc. 1.54 x 10-18 Pm-3 6.22 x 10-10 pm-3 Oe1 23 x 104 pm-3