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- What is the degeneracy of an h subshell? An n subshell?For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.
- What is the difference between continuous and discrete spectra?The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3 Evaluate: a Ap b Cq c Bs d Dq e A(Cr) f A(Dq)Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?
- The following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quantum numbers. a (5,4,0)(3,6,0)b (8,2,2)(9,2,2) c (7,4,2)(7,4,2)d (4,2,5)(3,2,5)The following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quatum numbers. a (0,0,0)(1,1,0)b (0,0,0)(1,0,0) c (3,2,1)(3,1,1)d (4,4,1)(2,4,1)Draw the graphical representations see Figure 11.15 of the possible values for l and ml for the first four energy levels of the 3-D rigid rotor. What are the degeneracies of each state?
- Draw, label, and explain the functions of the parts of a spectroscope.Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate the angular momentum p of the particle if p=i How does the angular momentum depend on the constant m?