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Unformatted text preview: HY28  N0. 8  d 1.
a) What are the possible values of Pfor n=6? b) What are the possible values of m,for 1:6? .c) What is the smallest possible value of n for whichFcan be 4? d) . What is the smallest possible! that can have a 2 component of 4h? 2. An electron is in the n=4, 1:3 state of hydrogen.
a) What is the length of the electron's angular momentum vector?
b) How many different possible 2 components can the angular momentum vector have? List the possible 2 components.
c) Would your answers to a) and b) change if the principle quantum number n were 5
instead of 4? ' 3. Show that the wave function ‘I’mo(r,6,¢) is properly normalized (see Table 7.1 of your
book). (*) 4. Show by direct substitution that the wave function corresponding to n=1,I=O, m,=0 is a
solution of Equation 7.3 (page 208 in your text book) corresponding to the groundstate
energy of hydrogen. 5. Find the values of the radius where the n=2, [:0 radial probability density has its
maximum values. 6. The mean or average value of the radius r can be found according to rm: ] rP(r)dr.
Show that the mean value of r for the ls state of hydrogen is (3/2)a0. (*) 0 . 09
(*) Use: 3 n —Clx d n .l
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 Spring '10
 MetCalfe
 Angular Momentum, smallest possible value, angular momentum vector, imam Ei mam

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