Term symbol for the ground state of a particular atom is quoted as *F, . The possible electronic confipuration is 9 2

Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene (see Example 4.7) and the n=2 wave function for the weakest bound electron, calculate the probability of finding the electron in an 0.1 interval centered midway between the two inner carbon atoms (that is, the center is at x=2.11 , so this interval is from x1=2.06 to x2=2.16 ). Then calculate the probability of finding the electron in an 0.1 interval centered midway between an end carbon atom and the carbon atom that is double-bonded to it in the Lewis dot structure. (You may calculate the appropriate integrals or estimate the relevant areas under the curve graphically.) Then recalculate the probabilities by approximating the integral as |( x 0)|2x , where x0 is evaluated in the middle of the range from x1 to x2 . Finally, explain why you can’t approximate the integral needed for Problem 37(a) in this way.

Photoelectron spectroscopy studies have determined the orbital energies for fluorine atoms to be 1s689eV2s34eV2p12eV Estimate the value of Zeff for F in each of these orbitals.

Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)

Explain why cyclopentadiene easily accepts an electron to become cyclopentadienyl anion C5H5, which is abbreviated Cp in organic or organometallic chemistry.

Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.

Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)

In the Brackett series, nlo=4. (a) Calculate the wavelength in nanometers of a transition from n=6 to n=4. (b) In what spectral region are these lines formed?

Consider the following transitions 1. n=3 to n=1 2. n=2 to n=33. n=4 to n=34. n=3 to n=5(a) For which of the transitions is energy absorbed? (b) For which of the transitions is energy emitted? (c) Which transitions involve the ground state? (d) Which transition absorbs the most energy? (e) Which transition emits the most energy?

Spectroscopic studies of Li also show that Zeff(2p)=1.02 . Estimate the energy of the 2p orbital of Li. Calculate the average distance of the electron from the nucleus in the 2p orbital of Li. Comparing your results with those in Problem 13 shows that the energy values differ by about 50%, whereas the average distances are nearly equal. Explain this observation.