Transcript Consider two electrons with orbital angular momentum

Consider two electrons with orbital angular momentum quantum
numbers ℓ1 and ℓ2. Adding angular momenta means adding vectors.
How can we determine the possible values of the quantum number L
for the sum of the two?
(A) We add the z-projection quantum numbers.
(B) We add the possible combinations of z-projection quantum numbers,
then determine the distinct ways of L to generate them.
(C) We add the two orbital angular momentum quantum numbers.
(D) We add the possible combinations of z-projection quantum numbers.
The L values that can generate them are the possible L values.
Consider two electrons with orbital angular momentum quantum
numbers ℓ1 and ℓ2. Adding angular momenta means adding vectors.
How can we determine the possible values of the quantum number L
for the sum of the two?
(A) We add the z-projection quantum numbers.
... that’s an ill defined recipe
(B) We add the possible combinations of z-projection quantum numbers,
then determine the distinct ways of L to generate them.
(C) We add the two orbital angular momentum quantum numbers. ...no
(D) We add the possible combinations of z-projection quantum numbers.
The L values that can generate them are the possible L values. ...no
Consider the wave functions for singlet and triplet states of
He(1s)(2p). Which state is lower in energy?
1
1
1s(1)2 p(2)  2 p(1)1s(2)  (1) (2)   (1) (2)

2
2
1
 1
 2  (1)  (2)   (1) (2) 

1
3
1s(1)2 p(2)  2 p(1)1s(2)    (1) (2)

2
 (1)  (2)


(A)Singlet
(B) Triplet
Consider the wave functions for singlet and triplet states of
He(1s)(2p). Which state is lower in energy?
1
1
1s(1)2 p(2)  2 p(1)1s(2)  (1) (2)   (1) (2)

2
2
1
 1
 2  (1)  (2)   (1) (2) 

1
3
1s(1)2 p(2)  2 p(1)1s(2)    (1) (2)

2
 (1)  (2)


(A)Singlet
(B) Triplet
3


 0 if r1  r2 , because of the “-” sign in the spatial
part of the wave function. One could say that triplet electrons
naturally avoid each other, leading to lower Coulomb repulsion.
General rule: for the same configuration, triplets are always lower
in energy than singlets. For He(1s)(2p), the difference is 0.254 eV .