2. (30 pts) A 11ydrogen atom is in the state Vza(r, О. ф )-R1 ( r...
2. (2.5 pts) What is the lifetime (in seconds) for the hydrogen atom to decay from then 3,1 = 0, mı = 0 state to the n = 2,1 = 1, ml = 0 state? Hint: Recall that the lifetime is the inverse of the Einstein coefficient A32. Also that r = r sin θ cos φ ex + r sin sin ф ey + r cos ez.
Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H atom, compute the most probable distance between electron and nucleus in the 1s state of H atom. (10 pts) With what probability the electron can be found anywhere farther than this most probable distance? Radial component of the hydrogen-like wavefunctions (20 points total) 2. (10 pts) By considering the radial component of the 1s orbital of H...
studying for my final, help 14) [5 pts) Calculate the most probable value of r for an electron in the ground state of the hydrogen atom. If P1s (r) = e-2rao, then evaluate the most probable value of r by setting 42 18 = 0 and solving for r. Sº ở d d a. ro= ao 0.6529 nm d. Yo = e. None the above
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p. [4] Consider a harmonic oscillator...
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the cross products #x f, #x θ, PX φ, θ 0, θ >< φ, and φ >< φ. (b) Express x, y and z in terms of, О and ф. (c) Check the divergence theorern for the function u = r , using for volume the sphere of radius 13] R, centered at the origin, i.e. show that dä -JyV-üö)dr.
Calculate <r> and the most probable value of radial function for the H atom in its ground state
--2-11x(t)+は111(t) 2. (10 pts.) If X(t) and the sample period. T. is selected to equal T-0. I, find Ф and Г in the ZOH equivalent discrete-time, state space representation. y(t)=[-1 1]x(t) , --2-11x(t)+は111(t) 2. (10 pts.) If X(t) and the sample period. T. is selected to equal T-0. I, find Ф and Г in the ZOH equivalent discrete-time, state space representation. y(t)=[-1 1]x(t) ,
Problem 8 (30 pts). The ground state wave function for the hydrogen atom is: W... (7,0,) - (a, 15pts) Find (-2) for an electron in this state. Find <x> and <x>
rrent 1 for R 40 Ω and R1-30 Ω for: No. 4 R1 30 V 6Ω R1 50 V 6Ω se Δ to Y transformation.
(18 pts) 10. Consider the circuit shown in the sketch. R1-30 Ω, R,- 2, and Ra -120n Ry 12요 a) What is the potential difference Va between points a and b and what is the potential Ve between points b and c Ans. Vab Vic b) What is the current through each resistor? Ans. 11- c) What is the current through the emf source (the battery)? Ans.