![]() ![]() Which are called $S$, $P$, and $D$ states respectively (because spectroscopists have weird terminology sometimes). In the case of the two p-orbital electrons, we have that $J_1 = 1/2$ and $J_2 = 1/2$, so the allowed values for $J$ are It's got nothing to do with the projection quantum numbers $m_J$. Note that here, $J_1$, $J_2$, and $J$ are the quantum numbers which relate to the magnitude of the angular momentum. ![]() $J$ is just a generic symbol for some source of angular momentum. In this case, the objective is to couple two sources of angular momentum: that of electron 1 with that of electron 2.įor any two sources of angular momentum with quantum numbers $J_1$ and $J_2$, the resulting sum can have quantum numbers Why use $l$ and $s$ instead of $m_l$ and $m_s$? It comes down to how angular momentum coupling is worked out. You are probably confusing it with $m_s$ which relates to the projection of the spin angular momentum and takes values between $-s, -s 1, \ldots, s$, i.e. Spin quantum numbers are always non-negative and for electrons is $1/2$. $s$ here is the spin quantum number, it is related to the magnitude of the spin angular momentum. We get the possible terms: $ \sideset^2$ configuration, both electrons are in p-orbitals, so they both have $l = 1$. Now the possible values for $L$ and $S$ are: We can ignore full orbitals, so we only look at $(2p)^2$. Carbon has the electron configuration $(1s)^2(2s)^2(2p)^2$. Currently studying how to "compute" term symbols. ![]()
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