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Chapter 41: Q. 7 (page 1207)

What areE and L (as a multiple ofh) of a hydrogen atom in the 6f state?

Short Answer

Expert verified

The hydrogen atom in the 6fstate isEn=鈭�0.3777eVandL=12魔.

Step by step solution

01

Given Information

We need to find are Eand L(as a multiple of h) of a hydrogen atom in the 6fstate.

02

Simplify

Finding value for Eand Lof a hydrogen atom in the 6fstate.

know that the hydrogen atom in the 6fstate is described by n=6an l=3.

Then,

En=鈭�13.6eVn2En=鈭�13.6eV62En=鈭�13.6eV36En=鈭�0.3777eV

Now, finding the value for angular momentum L:

L=ll+1魔L=33+1魔L=34魔L=12魔

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Most popular questions from this chapter

Suppose you have a machine that gives you pieces of candy when you push a button. Eighty percent of the time, pushing the button gets you two pieces of candy. Twenty percent of the time, pushing the button yields 10pieces. The average number of pieces per push is Navg=2脳0.80+10脳0.20=3.6. That is, 10pushes should get you, on average, 36pieces. Mathematically, the average value when the probabilities differ is Navg=鈭�(Ni脳Probabilityofi). We can do the same thing in quantum mechanics, with the difference that the sum becomes an integral. If you measured the distance of the electron from the proton in many hydrogen atoms,

you would get many values, as indicated by the radial probability density. But the average value of rwould be

ravg0=鈭�0鈭�rPr(r)dt

Calculate the average value of rin terms of aBfor the electron in the 1sand the 2pstates of hydrogen.

For an electron in the 1sstate of hydrogen, what is the probability of being in a spherical shell of thickness 0.010aBat distance (a) 12aB, (b) aB, and (c) 2aBfrom the proton?

FIGURE Q41.5shows the outcome of a Stern-Gerlach experiment with atoms of element X.

a. Do the peaks represent different values of the atom鈥檚 total angular momentum or different values of the z-component of its angular momentum? Explain.

b. What angular momentum quantum numbers characterize these four peaks?

The 5d鈫�3ptransition in the emission spectrum of sodium has a wavelength of 499nm.What is the energy of the5dstate ?

a. Draw a diagram similar to Figure 41.2 to show all the possible orientations of the angular momentum vector L鈫�for the case l=3. Label each L鈫�with the appropriate value of m.

b. What is the minimum angle between L鈫�and the z-axis?
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