Modern physics, quantum numbers, subshells

• fluidistic
In summary, in order to label the terms of an atom with a last subshell of np³, one must first find all possible values for $M_L$ and $M_S$, and then use these values to determine the possible values for $J$. The terms are then labeled in order of increasing energy, with the upper script representing the value of $2S+1$.
fluidistic
Gold Member

Homework Statement

Find all the terms of an atom whose last subshell is np³.

Homework Equations

$M_L=\sum _i m_{l _i}$
$M_S=\sum _i m_{s _i}$

The Attempt at a Solution

My professor did the same exercise but with np². Basically he wrotes all the possible quantum numbers for the atom:
1)$m_l=1$, $m_s=1/2$. 2)$m_l=0$, $m_s=1/2$. 3)$m_l=-1$, $m_s=1/2$
1')$m_l=1$, $m_s=-1/2$. 2')$m_l=0$, $m_s=-1/2$. 3')$m_l=-1$, $m_s=-1/2$
Then he calculated all the possible values for $M_L$ and $M_S$. There are 15 values in total.
After this, there is an obscure step to me (he counted I don't really know what) and went to the conclusion that the solution to the problem is $^1 D ^3 P ^1 S$. Where the upper script is worth $2S+1$.
So I did the same method as him for np³ (I guess this notation means that there are 3 electrons on the subshell p or an arbitrary n?). I got 20 values for $M_L$, $M_S$. I'm stuck at doing the obscure step now. I have all possible values for $M_L$ and $M_S$.
Can someone explain me what I should do next?
Another question is... since n seems arbitrary, can I for example take $n=1$, so that $l=0$ and $m_l=0$. My professor seems to have taken n=2 for some misterious reason to me. Does someone understand why?
Edit: since there are at least 3 electrons I guess I cannot take n=1, since at least n=2. Ah... n must equal 2... ok that's what I considered, good. So I'm stuck where I pointed out.

Last edited:
A:It looks like you are trying to label an atomic orbital. This can be done with the following equations:$M_L = \sum_i m_{l_i}$, and$M_S = \sum_i m_{s_i}$where there is one $m_{l_i}$ and one $m_{s_i}$ for each electron in the orbital.The terms of a np3 orbital are the same as for a np2 orbital, namely: $M_L = 0,\pm 1$$M_S = \frac{1}{2}, -\frac{1}{2}$You have listed these correctly.Now what does this mean? There are two possible values for the total angular momentum quantum number, $J$. The maximum value for $J$ is obtained when $M_L = M_S$, and the minimum value for $J$ is obtained when $M_L = -M_S$. Thus the possible values of $J$ are $J=M_L + M_S$ and $J=|M_L - M_S|$.For example, if $M_L = 1$ and $M_S = \frac{1}{2}$, then $J= \frac{3}{2}$ and $J = \frac{1}{2}$. So the terms of a np3 orbital are (in order of increasing energy):$^1D_2$, $^3P_2$, $^3P_1$, $^3P_0$, $^1S_0$

1. What is modern physics?

Modern physics is a branch of physics that studies the behavior of matter and energy at a subatomic level, using principles of quantum mechanics and relativity.

2. What are quantum numbers?

Quantum numbers are a set of four numbers used to describe the properties of an electron in an atom, including its energy level, orbital shape, orientation, and spin.

3. What are subshells?

Subshells, also known as energy sublevels, are groups of orbitals within an atom that have similar energy levels. They are labeled s, p, d, and f and correspond to the different shapes and orientations of electron orbitals.

4. How are quantum numbers related to subshells?

Quantum numbers determine the arrangement and properties of electrons within subshells. Each subshell has a specific set of quantum numbers that describe its energy level and orbital shape.

5. How does modern physics impact our daily lives?

Modern physics has led to important technological advancements, such as the development of computers, lasers, and medical imaging devices. It also helps us better understand the behavior of matter and energy, which has implications for fields like medicine, energy production, and materials science.

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