1) An electron has a wave function Ynim (r,0,0) = Cnr3 e-Kr Yım(0,0). a) What are...
An electron has a wave function Ynim (r,0,0) = (nr3 e-Kr Yım(0,0). a) What are nlm and their meaning. What additional quantum number added to nlm? b) Plot wave function and radial probability density for Is, 2s, 2p and comment on physical significance. c) Calculate 3s orbital magnetic moment in units of Bohr magnetron, use Bohr model and effective charge given in figure above. Compare it quantum version.
1) An electron has a wave function Ynim (r,0,0) = (yr e-Kr Yim (0,0). a) What are nelm and their meaning. What additional quantum number added to nlm? b) Plot wave function and radial probability density for Is, 2s 2p and comment on physical significance. c) Calculate 3s orbital magnetic moment in units of Bohr magnetron, use Bohr model and effective charge given in figure above. Compare it quantum version.
An electron has a wave function TnSn(r, 8, ) = Cnr3 e–Kr YSn(8, ) . What are nln and their meaning. What additional quantum number added to nln? Plot wave function and radial probability density for 1s, 2s, 2p and comment on physical significance. Calculate 3s orbital magnetic moment in units of Bohr magnetron, use Bohr model and effective charge given in figure above. Compare it quantum version.
Q-3 (25pts) The wave function of a ns electron in a hydrogen atom is r -r/(2a) y (,0,0)=1/27 927 (2-3) a) (10pts) Show that y function is already normalized. b) (10pts) Find the energy (En) of the electron. c) (5pts) Write the principle quantum number (n), orbital quantum number (?), and magnetic quantum number (mi) of the hydrogen electron state.
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
9. According to quantum mechanics, we must describe the position of electron in the hydrogen atom in terms of probabilities. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r?(2 pts) (b) What is the significance of the term 4nr2 in the radial probability functions for the s orbitals?(2 pts) (c) Make sketches of what you think the probability density as a function of r and...
Im particulary intrested in part (c)
The 2p (1) radial wave function of an electron in atomic hydrogen is R(r) Ab-2 where A is a constant. (a) Find the most probable value of r (that is, the most probable distance between the electron and the nucleus). (b) Find the average distance of the electron from the nucleus. (c) List all possible sets of quantum numbers that can describe an electron in this state
* *SHOW YOUR WORK & INCLUDE CORRECT UNITS for FULL CREDIT* e probability function P(r) associated from the radial wave function for an electron in the first excited Hydrogen ( 2p state n = 2 ) is given by: 4 P(r) = where ri-0.53x10""m (Bohr radius) a) Determine the three critical points associated with this radial probability function by evaluating: dP _=0 dr Regarding maxima and minima, deduce the most probable and least probable radial locations for the electron in...
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of finding 1-0? (c) Construct ψ(r, θ, φ) and another wave function with the same values of n and (azimuthal) quantum number, m+1 (d) Calculate the most probable value of r for an electron in the state corresponding to ψ(r, θ, φ) 1, but with...
The radial wave function for a 2s electron in a hydrogen atom is given by Pr(nm)? for 2s electron 1 r A2s(r) Je zao 3 (2 272a, z R ао 200 500 1000 r Calculate the r-value where the radial probability density of the 2s level is maximum. (Hint: Notice that P(r)=0 at r=2a, as shown in the figure).