Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。
Rohlf Chapter 9, #7,8,9,10,16,19,20,21
 
Rohlf 第9章，第7、8、9、10、16、19、20、21题

#7  Possible values of the total angular momentum J for Scandium
The electron configuration of Scandium is   from
Having a single outer 3d electron, we have l=2 and s=1/2 to work with.
The total angular momentum can then take the value j=5/2 and j=3/2
The actual angular momentum values from sqrt(j(j+1))hbar are then
J = sqrt(5/2(7/2))hbar=sqrt(35)*hbar/2 and J=sqrt(3/2(5/2))hbar= sqrt(15)*hbar/2

#7 Scandium的总角动量J的可能值。Scandium的电子构型为，其外层有一个3d电子，因此有l=2和s=1/2可以利用。总角动量可以取j=5/2和j=3/2的值。从sqrt(j(j+1))hbar计算得到的实际角动量值为J = sqrt(5/2(7/2))hbar=sqrt(35)*hbar/2和J=sqrt(3/2(5/2))hbar= sqrt(15)*hbar/2

#8  Possible total angular momentum values for a pair of 3d electrons, e.g. , just above Scandium.
With two electrons, each with l=2 and s=1/2, we can have total spin 0 or 1
The orbital angular momentum can take the values 0,1,2,3,4
Since the wavefunction for the system describes fermions, it must be antisymmetric.
The wavefunction is the product of the spin wavefunction and the spatial wavefunction,
so if the spin part is symmetric, space is antisymmetric and vice versa.
If spin is 1 and therefore symmetric, then l=1 or l=3 are the possibilities for the orbital wavefunction.

#8 3d电子对的可能总角动量值，例如在钪（Sc）以上。对于两个电子，每个电子的轨道角动量l=2，自旋s=1/2，总自旋可以是0或1。轨道角动量可以取0,1,2,3,4的值。由于系统的波函数描述的是费米子，它必须是反对称的。波函数是自旋波函数和空间波函数的乘积，因此如果自旋部分是对称的，空间部分必须是反对称的，反之亦然。如果自旋是1（对称的），则轨道波函数的可能值为l=1或l=3。

#9 Possible quantum numbers for outer electron configuration 2p13d1?
If l=1 for the p and l=2 for the d are combined, you could get L=1,2 or 3. Looks like to me that
spin can be either zero or 1, so j=0,1,2,3,4 possible.

#9 外层电子组态 2p13d1 的可能量子数？如果 p 电子的 l=1 和 d 电子的 l=2 结合，你可能得到 L=1,2 或 3。看起来自旋可以是零或 1，因此 j=0,1,2,3,4 可能。

#10. For two electrons in d subshell, what values for z-component of angular momentum possible?
The orbital angular momentum can stretch from 0 to 4. For S=0 it can take L=0,2,4 and for S=1, L=1,3.
So the total angular momentum can take values 0,1,2,3,4. Mj can then take -4,-3, … 2,3,4.

对于d轨道的两个电子，角动量的z分量可能的值有哪些？轨道角动量可以取从0到4的值。当S=0时，L可以取0,2,4；当S=1时，L可以取1,3。因此，总角动量可以取0,1,2,3,4。Mj则可以取-4,-3,…,2,3,4。

#16 Energy level diagram for silicon
With two outer 3p electrons, the energy levels are expected to be very much like those for carbon
shown in Figure 9-12, p269. My guess is a reproduction of the carbon level diagram
with all the principal quantum numbers jogged up by one. Expect that the ground
state is a 3p triplet state, and that of the other two 3p states, the one with the higher total angular
momentum (j=2) will be lower. Sp3 states could be expected as in carbon.

#16 硅的能级图。拥有两个外层3p电子时，其能级预计会非常类似于图9-12中所示的碳的能级图（第269页）。我的猜测是，这是一张碳的能级图，所有主量子数都提高了一位。预计基态是3p三重态，而其他两个3p态中，总角动量（j=2）较高的那个会更低。可能预期出现sp³态，如同碳的情况。

#19 Predict splitting for Stern-Gerlach experiment with other atoms.
No splitting: No electrons outside of closed shells, so the noble gases should exhibit no splitting.
Threefold splitting: Triplet state, spin=1. Can occur with two outer electrons, like carbon and silicon.
Fourfold splitting would come with spin=3/2, which could come with three electrons, like nitrogen.

#19 预测施特恩-格拉赫实验中其他原子的分裂情况。无分裂：原子外层电子壳层闭合，因此惰性气体应无分裂。三重分裂：三重态，自旋=1。当有两个外层电子时可能发生，如碳和硅。四重分裂将出现在自旋=3/2的情况下，这可能需要三个外层电子，如氮。

#20  Magnetic splitting with a 3d 5/2 state.
The number of magnetic levels is 2j+1 = 6

#20 具有3d 5/2态的磁分裂。磁能级数目为2j+1 = 6

#21. Splitting of a 2p state in a strong magnetic field.
The strong field magnetic splitting (Paschen-Back effect) depends upon ml + 2ms.
You look at the orbital and spin values separately, then combine. The values for
ml are -1,0,1 and the values of 2ms are -1 and 1. The possible combinations are
 -2,-1,0,1,2.  Since the splitting is (ml+2ms)* Bohr magneton* magnetic field in Tesla
Then the splitting is numerically equal to the quantum numbers -2,-1,0,1,2 times the
Bohr magneton.
This gives -11.8, -5.9, 0, 5.9, 11.8 times 1E-5 eV in a 1 Tesla field.
 

#21. 在强磁场中2p态的分裂。强磁场中的磁分裂（帕森-贝克效应）取决于ml + 2ms。你应分别考虑轨道和自旋值，然后结合起来。ml的可能值为-1,0,1，而2ms的可能值为-1和1。可能的组合为-2,-1,0,1,2。由于分裂值为(ml+2ms)*玻尔磁子*磁感应强度（单位为特斯拉）。因此，分裂值数值上等于量子数-2,-1,0,1,2乘以玻尔磁子。在1特斯拉磁场中，这给出-11.8, -5.9, 0, 5.9, 11.8倍的1E-5 eV。