In the spherical coordinates, the spin-less electron radial wave functions of the two lowest energy states (i.e. n= 1 and 2) of the time-independent Schroedinger equation for the hydrogen atom are known to be: R,(r) =2a, -3/2-rlao e and R,(r) = (2a,) 2 -3/2 2 r ,-r/2a, le , respectively, where a is the Bohr radius. (a) What are the algebraic expressions of the total wave functions, @(n,l, m,), for P (1,0,0), 9(2,0,0), and (2,1,0), respectively? (b) If one includes the electron spin, how many states are available for n= 2? Show your work.
In the spherical coordinates, the spin-less electron radial wave functions of the two lowest energy states (i.e. n= 1 and 2) of the time-independent Schroedinger equation for the hydrogen atom are known to be: R,(r) =2a, -3/2-rlao e and R,(r) = (2a,) 2 -3/2 2 r ,-r/2a, le , respectively, where a is the Bohr radius. (a) What are the algebraic expressions of the total wave functions, @(n,l, m,), for P (1,0,0), 9(2,0,0), and (2,1,0), respectively? (b) If one includes the electron spin, how many states are available for n= 2? Show your work.
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Transcribed Image Text:In the spherical coordinates, the spin-less electron radial wave functions of the two
lowest energy states (i.e. n= 1 and 2) of the time-independent Schroedinger equation for
the hydrogen atom are known to be:
-3/2
R,(r) = 2a
'erlao
and R,(r) = (2a,)
-r/2a,
e
respectively, where a, is
the Bohr radius.
(a) What are the algebraic expressions of the total wave functions, @ (n,l,m,), for
P (1,0,0), 9(2,0,0), and (2,1,0), respectively?
(b) If one includes the electron spin, how many states are available for n= 2? Show your
work.
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